Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 6 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/6]Find\ the\ 4th\ derivative\ of\ function\ sin(x)sin(x)sin(x) - sin(sin(sin(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{3}(x) - sin(sin(sin(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{3}(x) - sin(sin(sin(x)))\right)}{dx}\\=&3sin^{2}(x)cos(x) - cos(sin(sin(x)))cos(sin(x))cos(x)\\=&3sin^{2}(x)cos(x) - cos(sin(sin(x)))cos(x)cos(sin(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3sin^{2}(x)cos(x) - cos(sin(sin(x)))cos(x)cos(sin(x))\right)}{dx}\\=&3*2sin(x)cos(x)cos(x) + 3sin^{2}(x)*-sin(x) - -sin(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos(sin(x)) - cos(sin(sin(x)))*-sin(x)cos(sin(x)) - cos(sin(sin(x)))cos(x)*-sin(sin(x))cos(x)\\=&sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + sin(x)cos(sin(sin(x)))cos(sin(x)) + sin(sin(x))cos(sin(sin(x)))cos^{2}(x) + 6sin(x)cos^{2}(x) - 3sin^{3}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + sin(x)cos(sin(sin(x)))cos(sin(x)) + sin(sin(x))cos(sin(sin(x)))cos^{2}(x) + 6sin(x)cos^{2}(x) - 3sin^{3}(x)\right)}{dx}\\=&cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(x)cos^{2}(sin(x)) + sin(sin(sin(x)))*-2cos(x)sin(x)cos^{2}(sin(x)) + sin(sin(sin(x)))cos^{2}(x)*-2cos(sin(x))sin(sin(x))cos(x) + cos(x)cos(sin(sin(x)))cos(sin(x)) + sin(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x)) + sin(x)cos(sin(sin(x)))*-sin(sin(x))cos(x) + cos(sin(x))cos(x)cos(sin(sin(x)))cos^{2}(x) + sin(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(x) + sin(sin(x))cos(sin(sin(x)))*-2cos(x)sin(x) + 6cos(x)cos^{2}(x) + 6sin(x)*-2cos(x)sin(x) - 3*3sin^{2}(x)cos(x)\\=&cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) - 2sin(x)sin(sin(sin(x)))cos(x)cos^{2}(sin(x)) - 2sin(sin(sin(x)))sin(sin(x))cos(sin(x))cos^{3}(x) + cos(x)cos(sin(sin(x)))cos(sin(x)) - sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x)) - sin(x)sin(sin(x))cos(x)cos(sin(sin(x))) + cos^{3}(x)cos(sin(x))cos(sin(sin(x))) - sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x)) - 2sin(x)sin(sin(x))cos(sin(sin(x)))cos(x) + 6cos^{3}(x) - 21sin^{2}(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) - 2sin(x)sin(sin(sin(x)))cos(x)cos^{2}(sin(x)) - 2sin(sin(sin(x)))sin(sin(x))cos(sin(x))cos^{3}(x) + cos(x)cos(sin(sin(x)))cos(sin(x)) - sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x)) - sin(x)sin(sin(x))cos(x)cos(sin(sin(x))) + cos^{3}(x)cos(sin(x))cos(sin(sin(x))) - sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x)) - 2sin(x)sin(sin(x))cos(sin(sin(x)))cos(x) + 6cos^{3}(x) - 21sin^{2}(x)cos(x)\right)}{dx}\\=&-sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x)) + cos(sin(sin(x)))*-3cos^{2}(x)sin(x)cos^{3}(sin(x)) + cos(sin(sin(x)))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x) - 2cos(x)sin(sin(sin(x)))cos(x)cos^{2}(sin(x)) - 2sin(x)cos(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos^{2}(sin(x)) - 2sin(x)sin(sin(sin(x)))*-sin(x)cos^{2}(sin(x)) - 2sin(x)sin(sin(sin(x)))cos(x)*-2cos(sin(x))sin(sin(x))cos(x) - 2cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos(sin(x))cos^{3}(x) - 2sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos^{3}(x) - 2sin(sin(sin(x)))sin(sin(x))*-sin(sin(x))cos(x)cos^{3}(x) - 2sin(sin(sin(x)))sin(sin(x))cos(sin(x))*-3cos^{2}(x)sin(x) + -sin(x)cos(sin(sin(x)))cos(sin(x)) + cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x)) + cos(x)cos(sin(sin(x)))*-sin(sin(x))cos(x) - cos(sin(sin(x)))cos(sin(x))cos(x)sin(x)cos(x)cos^{2}(sin(x)) - sin(sin(sin(x)))cos(x)cos(x)cos^{2}(sin(x)) - sin(sin(sin(x)))sin(x)*-sin(x)cos^{2}(sin(x)) - sin(sin(sin(x)))sin(x)cos(x)*-2cos(sin(x))sin(sin(x))cos(x) - cos(x)sin(sin(x))cos(x)cos(sin(sin(x))) - sin(x)cos(sin(x))cos(x)cos(x)cos(sin(sin(x))) - sin(x)sin(sin(x))*-sin(x)cos(sin(sin(x))) - sin(x)sin(sin(x))cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x) + -3cos^{2}(x)sin(x)cos(sin(x))cos(sin(sin(x))) + cos^{3}(x)*-sin(sin(x))cos(x)cos(sin(sin(x))) + cos^{3}(x)cos(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x) - cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos^{3}(x)cos(sin(x)) - sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos(sin(x)) - sin(sin(sin(x)))sin(sin(x))*-3cos^{2}(x)sin(x)cos(sin(x)) - sin(sin(sin(x)))sin(sin(x))cos^{3}(x)*-sin(sin(x))cos(x) - 2cos(x)sin(sin(x))cos(sin(sin(x)))cos(x) - 2sin(x)cos(sin(x))cos(x)cos(sin(sin(x)))cos(x) - 2sin(x)sin(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(x) - 2sin(x)sin(sin(x))cos(sin(sin(x)))*-sin(x) + 6*-3cos^{2}(x)sin(x) - 21*2sin(x)cos(x)cos(x) - 21sin^{2}(x)*-sin(x)\\=& - 5sin(x)cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x)) - 3sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(x))) - sin(x)cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 6sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(x))) - 3sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x)) + 6sin(sin(sin(x)))sin(x)sin(sin(x))cos(sin(x))cos^{2}(x) + 4sin(sin(x))sin(sin(sin(x)))sin(x)cos(sin(x))cos^{2}(x) - sin(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x)) - 4sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + 2sin(sin(x))sin(x)sin(sin(sin(x)))cos(sin(x))cos^{2}(x) + 3sin(sin(sin(x)))sin(x)sin(sin(x))cos^{2}(x)cos(sin(x)) - 3sin(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) + sin(sin(sin(x)))sin^{2}(x)cos^{2}(sin(x)) + 3sin^{2}(sin(x))sin(sin(sin(x)))cos^{4}(x) - 4sin(sin(x))cos^{2}(x)cos(sin(sin(x))) + 3sin^{2}(x)sin(sin(x))cos(sin(sin(x))) + 3sin(sin(x))sin(x)sin(sin(sin(x)))cos^{2}(x)cos(sin(x)) - sin(sin(x))cos^{4}(x)cos(sin(sin(x))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x) + 2sin^{2}(x)sin(sin(sin(x)))cos^{2}(sin(x)) - sin(x)cos(sin(sin(x)))cos(sin(x)) - 60sin(x)cos^{2}(x) + 21sin^{3}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/6]Find\ the\ 4th\ derivative\ of\ function\ cos(x)cos(x)cos(x) - cos(cos(cos(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{3}(x) - cos(cos(cos(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos^{3}(x) - cos(cos(cos(x)))\right)}{dx}\\=&-3cos^{2}(x)sin(x) - -sin(cos(cos(x)))*-sin(cos(x))*-sin(x)\\=&-3sin(x)cos^{2}(x) + sin(cos(x))sin(x)sin(cos(cos(x)))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3sin(x)cos^{2}(x) + sin(cos(x))sin(x)sin(cos(cos(x)))\right)}{dx}\\=&-3cos(x)cos^{2}(x) - 3sin(x)*-2cos(x)sin(x) + cos(cos(x))*-sin(x)sin(x)sin(cos(cos(x))) + sin(cos(x))cos(x)sin(cos(cos(x))) + sin(cos(x))sin(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x)\\=&-3cos^{3}(x) + 6sin^{2}(x)cos(x) - sin^{2}(x)sin(cos(cos(x)))cos(cos(x)) + sin(cos(x))sin(cos(cos(x)))cos(x) + sin^{2}(cos(x))sin^{2}(x)cos(cos(cos(x)))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -3cos^{3}(x) + 6sin^{2}(x)cos(x) - sin^{2}(x)sin(cos(cos(x)))cos(cos(x)) + sin(cos(x))sin(cos(cos(x)))cos(x) + sin^{2}(cos(x))sin^{2}(x)cos(cos(cos(x)))\right)}{dx}\\=&-3*-3cos^{2}(x)sin(x) + 6*2sin(x)cos(x)cos(x) + 6sin^{2}(x)*-sin(x) - 2sin(x)cos(x)sin(cos(cos(x)))cos(cos(x)) - sin^{2}(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(cos(x)) - sin^{2}(x)sin(cos(cos(x)))*-sin(cos(x))*-sin(x) + cos(cos(x))*-sin(x)sin(cos(cos(x)))cos(x) + sin(cos(x))cos(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(x) + sin(cos(x))sin(cos(cos(x)))*-sin(x) + 2sin(cos(x))cos(cos(x))*-sin(x)sin^{2}(x)cos(cos(cos(x))) + sin^{2}(cos(x))*2sin(x)cos(x)cos(cos(cos(x))) + sin^{2}(cos(x))sin^{2}(x)*-sin(cos(cos(x)))*-sin(cos(x))*-sin(x)\\=&21sin(x)cos^{2}(x) - 2sin(x)sin(cos(cos(x)))cos(x)cos(cos(x)) - sin(cos(x))sin(x)sin(cos(cos(x))) - sin(cos(x))sin^{3}(x)cos(cos(cos(x)))cos(cos(x)) - sin(cos(cos(x)))sin^{3}(x)sin(cos(x)) - sin(x)sin(cos(cos(x)))cos(cos(x))cos(x) + sin^{2}(cos(x))sin(x)cos(cos(cos(x)))cos(x) + 2sin(x)sin^{2}(cos(x))cos(x)cos(cos(cos(x))) - 2sin^{3}(x)sin(cos(x))cos(cos(x))cos(cos(cos(x))) - sin^{3}(cos(x))sin(cos(cos(x)))sin^{3}(x) - 6sin^{3}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 21sin(x)cos^{2}(x) - 2sin(x)sin(cos(cos(x)))cos(x)cos(cos(x)) - sin(cos(x))sin(x)sin(cos(cos(x))) - sin(cos(x))sin^{3}(x)cos(cos(cos(x)))cos(cos(x)) - sin(cos(cos(x)))sin^{3}(x)sin(cos(x)) - sin(x)sin(cos(cos(x)))cos(cos(x))cos(x) + sin^{2}(cos(x))sin(x)cos(cos(cos(x)))cos(x) + 2sin(x)sin^{2}(cos(x))cos(x)cos(cos(cos(x))) - 2sin^{3}(x)sin(cos(x))cos(cos(x))cos(cos(cos(x))) - sin^{3}(cos(x))sin(cos(cos(x)))sin^{3}(x) - 6sin^{3}(x)\right)}{dx}\\=&21cos(x)cos^{2}(x) + 21sin(x)*-2cos(x)sin(x) - 2cos(x)sin(cos(cos(x)))cos(x)cos(cos(x)) - 2sin(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(x)cos(cos(x)) - 2sin(x)sin(cos(cos(x)))*-sin(x)cos(cos(x)) - 2sin(x)sin(cos(cos(x)))cos(x)*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin(x)sin(cos(cos(x))) - sin(cos(x))cos(x)sin(cos(cos(x))) - sin(cos(x))sin(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin^{3}(x)cos(cos(cos(x)))cos(cos(x)) - sin(cos(x))*3sin^{2}(x)cos(x)cos(cos(cos(x)))cos(cos(x)) - sin(cos(x))sin^{3}(x)*-sin(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x) - cos(cos(cos(x)))*-sin(cos(x))*-sin(x)sin^{3}(x)sin(cos(x)) - sin(cos(cos(x)))*3sin^{2}(x)cos(x)sin(cos(x)) - sin(cos(cos(x)))sin^{3}(x)cos(cos(x))*-sin(x) - cos(x)sin(cos(cos(x)))cos(cos(x))cos(x) - sin(x)cos(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(cos(x))cos(x) - sin(x)sin(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(x) - sin(x)sin(cos(cos(x)))cos(cos(x))*-sin(x) + 2sin(cos(x))cos(cos(x))*-sin(x)sin(x)cos(cos(cos(x)))cos(x) + sin^{2}(cos(x))cos(x)cos(cos(cos(x)))cos(x) + sin^{2}(cos(x))sin(x)*-sin(cos(cos(x)))*-sin(cos(x))*-sin(x)cos(x) + sin^{2}(cos(x))sin(x)cos(cos(cos(x)))*-sin(x) + 2cos(x)sin^{2}(cos(x))cos(x)cos(cos(cos(x))) + 2sin(x)*2sin(cos(x))cos(cos(x))*-sin(x)cos(x)cos(cos(cos(x))) + 2sin(x)sin^{2}(cos(x))*-sin(x)cos(cos(cos(x))) + 2sin(x)sin^{2}(cos(x))cos(x)*-sin(cos(cos(x)))*-sin(cos(x))*-sin(x) - 2*3sin^{2}(x)cos(x)sin(cos(x))cos(cos(x))cos(cos(cos(x))) - 2sin^{3}(x)cos(cos(x))*-sin(x)cos(cos(x))cos(cos(cos(x))) - 2sin^{3}(x)sin(cos(x))*-sin(cos(x))*-sin(x)cos(cos(cos(x))) - 2sin^{3}(x)sin(cos(x))cos(cos(x))*-sin(cos(cos(x)))*-sin(cos(x))*-sin(x) - 3sin^{2}(cos(x))cos(cos(x))*-sin(x)sin(cos(cos(x)))sin^{3}(x) - sin^{3}(cos(x))cos(cos(cos(x)))*-sin(cos(x))*-sin(x)sin^{3}(x) - sin^{3}(cos(x))sin(cos(cos(x)))*3sin^{2}(x)cos(x) - 6*3sin^{2}(x)cos(x)\\=&21cos^{3}(x) - 3sin^{2}(x)sin(cos(x))cos(x)cos(cos(cos(x)))cos(cos(x)) - 3sin(cos(cos(x)))cos^{2}(x)cos(cos(x)) - 2sin(cos(x))sin^{2}(x)cos(cos(cos(x)))cos(x)cos(cos(x)) - 6sin^{2}(x)sin(cos(x))cos(x)cos(cos(x))cos(cos(cos(x))) - 3sin(cos(cos(x)))sin^{2}(x)sin(cos(x))cos(x) - sin(cos(x))sin^{2}(x)cos(cos(cos(x)))cos(cos(x))cos(x) - 2sin^{2}(x)sin(cos(x))cos(cos(x))cos(cos(cos(x)))cos(x) + 3sin^{4}(x)cos^{2}(cos(x))cos(cos(cos(x))) - 4sin(cos(x))sin^{2}(x)cos(cos(x))cos(x)cos(cos(cos(x))) + 3sin^{2}(cos(x))sin(cos(cos(x)))sin^{4}(x)cos(cos(x)) - 2sin^{4}(x)sin^{2}(cos(x))cos(cos(cos(x))) - 3sin^{2}(x)sin(cos(cos(x)))sin(cos(x))cos(x) + sin^{4}(x)sin(cos(cos(x)))cos(cos(x)) - sin(cos(x))sin(cos(cos(x)))cos(x) - 2sin^{2}(cos(x))sin^{2}(x)cos(cos(cos(x))) + 3sin^{2}(cos(x))cos^{2}(x)cos(cos(cos(x))) - 3sin^{3}(cos(x))sin(cos(cos(x)))sin^{2}(x)cos(x) + 4sin^{2}(x)sin(cos(cos(x)))cos(cos(x)) - 2sin^{2}(x)sin^{2}(cos(x))cos(cos(cos(x))) - 60sin^{2}(x)cos(x) - 2sin^{2}(cos(x))sin^{4}(x)cos(cos(cos(x))) + 3sin^{4}(x)sin^{2}(cos(x))sin(cos(cos(x)))cos(cos(x)) - sin^{4}(cos(x))sin^{4}(x)cos(cos(cos(x))) - 3sin^{3}(cos(x))sin^{2}(x)sin(cos(cos(x)))cos(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[3/6]Find\ the\ 4th\ derivative\ of\ function\ tan(x)tan(x)tan(x) - tan(tan(tan(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan^{3}(x) - tan(tan(tan(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan^{3}(x) - tan(tan(tan(x)))\right)}{dx}\\=&3tan^{2}(x)sec^{2}(x)(1) - sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))\\=&3tan^{2}(x)sec^{2}(x) - sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3tan^{2}(x)sec^{2}(x) - sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x))\right)}{dx}\\=&3*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 3tan^{2}(x)*2sec^{2}(x)tan(x) - 2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(x)sec^{2}(tan(x)) - sec^{2}(tan(tan(x)))*2sec^{2}(x)tan(x)sec^{2}(tan(x)) - sec^{2}(tan(tan(x)))sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)\\=& - 2tan(x)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 2tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 2tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) + 6tan(x)sec^{4}(x) + 6tan^{3}(x)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2tan(x)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 2tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 2tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) + 6tan(x)sec^{4}(x) + 6tan^{3}(x)sec^{2}(x)\right)}{dx}\\=& - 2sec^{2}(x)(1)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 2tan(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(x)sec^{2}(tan(x)) - 2tan(x)sec^{2}(tan(tan(x)))*2sec^{2}(x)tan(x)sec^{2}(tan(x)) - 2tan(x)sec^{2}(tan(tan(x)))sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) - 2sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 2tan(tan(tan(x)))*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(x)sec^{4}(tan(x)) - 2tan(tan(tan(x)))sec^{2}(tan(tan(x)))*4sec^{4}(x)tan(x)sec^{4}(tan(x)) - 2tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) - 2sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 2tan(tan(x))*4sec^{4}(x)tan(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 2tan(tan(x))sec^{4}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x)) - 2tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 6sec^{2}(x)(1)sec^{4}(x) + 6tan(x)*4sec^{4}(x)tan(x) + 6*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 6tan^{3}(x)*2sec^{2}(x)tan(x)\\=& - 2sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 4tan(tan(tan(x)))tan(x)sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 4tan^{2}(x)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 12tan(x)tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 2sec^{4}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 4tan^{2}(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 8tan(x)tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 8tan(tan(tan(x)))tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 2sec^{6}(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))tan(tan(x))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 4tan^{2}(tan(x))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) + 6sec^{6}(x) + 42tan^{2}(x)sec^{4}(x) + 12tan^{4}(x)sec^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 2sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 4tan(tan(tan(x)))tan(x)sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 4tan^{2}(x)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 12tan(x)tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 2sec^{4}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 4tan^{2}(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 8tan(x)tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 8tan(tan(tan(x)))tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 2sec^{6}(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))tan(tan(x))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 4tan^{2}(tan(x))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) + 6sec^{6}(x) + 42tan^{2}(x)sec^{4}(x) + 12tan^{4}(x)sec^{2}(x)\right)}{dx}\\=& - 2*4sec^{4}(x)tan(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 2sec^{4}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x)) - 2sec^{4}(x)sec^{2}(tan(tan(x)))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) - 4sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))tan(x)sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 4tan(tan(tan(x)))sec^{2}(x)(1)sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 4tan(tan(tan(x)))tan(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(x)sec^{4}(tan(x)) - 4tan(tan(tan(x)))tan(x)sec^{2}(tan(tan(x)))*4sec^{4}(x)tan(x)sec^{4}(tan(x)) - 4tan(tan(tan(x)))tan(x)sec^{2}(tan(tan(x)))sec^{4}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) - 4*2tan(x)sec^{2}(x)(1)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 4tan^{2}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(x)sec^{2}(tan(x)) - 4tan^{2}(x)sec^{2}(tan(tan(x)))*2sec^{2}(x)tan(x)sec^{2}(tan(x)) - 4tan^{2}(x)sec^{2}(tan(tan(x)))sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) - 12sec^{2}(x)(1)tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 12tan(x)sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 12tan(x)tan(tan(x))*4sec^{4}(x)tan(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 12tan(x)tan(tan(x))sec^{4}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x)) - 12tan(x)tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) - 2*4sec^{4}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{6}(tan(x)) - 2sec^{4}(tan(tan(x)))*6sec^{6}(x)tan(x)sec^{6}(tan(x)) - 2sec^{4}(tan(tan(x)))sec^{6}(x)*6sec^{6}(tan(x))tan(tan(x))sec^{2}(x)(1) - 4*2tan(tan(tan(x)))sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 4tan^{2}(tan(tan(x)))*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{6}(tan(x)) - 4tan^{2}(tan(tan(x)))sec^{2}(tan(tan(x)))*6sec^{6}(x)tan(x)sec^{6}(tan(x)) - 4tan^{2}(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{6}(x)*6sec^{6}(tan(x))tan(tan(x))sec^{2}(x)(1) - 8sec^{2}(x)(1)tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 8tan(x)sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 8tan(x)tan(tan(tan(x)))*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(x)sec^{4}(tan(x)) - 8tan(x)tan(tan(tan(x)))sec^{2}(tan(tan(x)))*4sec^{4}(x)tan(x)sec^{4}(tan(x)) - 8tan(x)tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) - 8sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 8tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 8tan(tan(tan(x)))tan(tan(x))*6sec^{6}(x)tan(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 8tan(tan(tan(x)))tan(tan(x))sec^{6}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(tan(x)) - 8tan(tan(tan(x)))tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) - 2*6sec^{6}(x)tan(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 2sec^{6}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{2}(tan(tan(x))) - 2sec^{6}(x)sec^{4}(tan(x))*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1)) - 4sec^{2}(tan(tan(x)))(sec^{2}(tan(x))(sec^{2}(x)(1)))tan(tan(x))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))tan(tan(x))*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{6}(x)sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))tan(tan(x))sec^{4}(tan(x))*6sec^{6}(x)tan(x)sec^{2}(tan(tan(x))) - 4tan(tan(tan(x)))tan(tan(x))sec^{4}(tan(x))sec^{6}(x)*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1)) - 4*2tan(tan(x))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) - 4tan^{2}(tan(x))*2sec^{2}(tan(tan(x)))tan(tan(tan(x)))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{2}(tan(x)) - 4tan^{2}(tan(x))sec^{2}(tan(tan(x)))*6sec^{6}(x)tan(x)sec^{2}(tan(x)) - 4tan^{2}(tan(x))sec^{2}(tan(tan(x)))sec^{6}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 6*6sec^{6}(x)tan(x) + 42*2tan(x)sec^{2}(x)(1)sec^{4}(x) + 42tan^{2}(x)*4sec^{4}(x)tan(x) + 12*4tan^{3}(x)sec^{2}(x)(1)sec^{2}(x) + 12tan^{4}(x)*2sec^{2}(x)tan(x)\\=& - 24tan(x)sec^{6}(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 16tan(tan(tan(x)))sec^{4}(tan(tan(x)))sec^{8}(x)sec^{8}(tan(x)) - 4tan(x)sec^{6}(x)sec^{6}(tan(x))sec^{4}(tan(tan(x))) - 20tan(x)sec^{4}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 12tan(tan(tan(x)))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 32tan(x)tan^{2}(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 24tan(tan(tan(x)))tan^{2}(x)sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 16tan(tan(x))tan(x)tan(tan(tan(x)))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 16tan(tan(tan(x)))sec^{8}(x)sec^{6}(tan(x))sec^{2}(tan(tan(x))) - 8tan^{3}(x)sec^{2}(tan(tan(x)))sec^{2}(x)sec^{2}(tan(x)) - 56tan^{2}(x)tan(tan(x))sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 12tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 24tan(tan(x))tan(x)tan(tan(tan(x)))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 24tan^{2}(tan(x))tan(x)sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) - 16tan(x)sec^{4}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) - 12tan(tan(x))sec^{8}(x)sec^{6}(tan(x))sec^{4}(tan(tan(x))) - 4tan(tan(tan(x)))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 8tan^{3}(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{8}(x)sec^{8}(tan(x)) - 24tan^{2}(tan(tan(x)))tan(tan(x))sec^{8}(x)sec^{2}(tan(tan(x)))sec^{6}(tan(x)) - 16tan^{2}(tan(tan(x)))tan(x)sec^{2}(tan(tan(x)))sec^{6}(x)sec^{6}(tan(x)) - 32tan^{2}(x)tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{4}(x)sec^{4}(tan(x)) - 32tan(tan(x))tan(tan(tan(x)))tan(x)sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 8tan(tan(x))sec^{8}(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 48tan(tan(tan(x)))tan(x)tan(tan(x))sec^{6}(x)sec^{2}(tan(tan(x)))sec^{4}(tan(x)) - 16tan(tan(x))tan^{2}(tan(tan(x)))sec^{6}(tan(x))sec^{8}(x)sec^{2}(tan(tan(x))) - 32tan^{2}(tan(x))tan(tan(tan(x)))sec^{2}(tan(tan(x)))sec^{8}(x)sec^{4}(tan(x)) - 8tan(tan(x))sec^{4}(tan(x))sec^{8}(x)sec^{2}(tan(tan(x))) - 4tan(tan(x))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) - 16tan^{2}(tan(x))tan(tan(tan(x)))sec^{8}(x)sec^{4}(tan(x))sec^{2}(tan(tan(x))) - 24tan(tan(tan(x)))tan(x)tan(tan(x))sec^{4}(tan(x))sec^{6}(x)sec^{2}(tan(tan(x))) - 8tan(tan(x))tan^{2}(tan(tan(x)))sec^{6}(tan(x))sec^{2}(tan(tan(x)))sec^{8}(x) - 12tan(tan(x))sec^{8}(x)sec^{4}(tan(tan(x)))sec^{6}(tan(x)) - 8tan(tan(tan(x)))tan^{2}(tan(x))sec^{2}(tan(tan(x)))sec^{8}(x)sec^{4}(tan(x)) - 24tan(x)tan^{2}(tan(x))sec^{2}(tan(tan(x)))sec^{6}(x)sec^{2}(tan(x)) - 8tan^{3}(tan(x))sec^{8}(x)sec^{2}(tan(tan(x)))sec^{2}(tan(x)) + 120tan(x)sec^{6}(x) + 216tan^{3}(x)sec^{4}(x) + 24tan^{5}(x)sec^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[4/6]Find\ the\ 4th\ derivative\ of\ function\ cot(x)cot(x)cot(x) - cot(cot(cot(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cot^{3}(x) - cot(cot(cot(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cot^{3}(x) - cot(cot(cot(x)))\right)}{dx}\\=&-3cot^{2}(x)csc^{2}(x) - -csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)\\=&-3cot^{2}(x)csc^{2}(x) + csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x)))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3cot^{2}(x)csc^{2}(x) + csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x)))\right)}{dx}\\=&-3*-2cot(x)csc^{2}(x)csc^{2}(x) - 3cot^{2}(x)*-2csc^{2}(x)cot(x) + -2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(x)csc^{2}(cot(cot(x))) + csc^{2}(cot(x))*-2csc^{2}(x)cot(x)csc^{2}(cot(cot(x))) + csc^{2}(cot(x))csc^{2}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)\\=& - 2cot(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) + 2cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 2cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 6cot(x)csc^{4}(x) + 6cot^{3}(x)csc^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2cot(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) + 2cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 2cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 6cot(x)csc^{4}(x) + 6cot^{3}(x)csc^{2}(x)\right)}{dx}\\=& - 2*-csc^{2}(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) - 2cot(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(x)csc^{2}(cot(cot(x))) - 2cot(x)csc^{2}(cot(x))*-2csc^{2}(x)cot(x)csc^{2}(cot(cot(x))) - 2cot(x)csc^{2}(cot(x))csc^{2}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 2*-csc^{2}(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 2cot(cot(x))*-4csc^{4}(x)cot(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 2cot(cot(x))csc^{4}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) + 2cot(cot(x))csc^{4}(x)csc^{2}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 2*-csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) - 2cot(cot(cot(x)))*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(cot(x))) - 2cot(cot(cot(x)))csc^{4}(cot(x))*-4csc^{4}(x)cot(x)csc^{2}(cot(cot(x))) - 2cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 6*-csc^{2}(x)csc^{4}(x) + 6cot(x)*-4csc^{4}(x)cot(x) + 6*-3cot^{2}(x)csc^{2}(x)csc^{2}(x) + 6cot^{3}(x)*-2csc^{2}(x)cot(x)\\=&2csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(x))cot(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))cot(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 2csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot(x)cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(cot(x))csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))cot(cot(x))csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) + 2csc^{6}(cot(x))csc^{6}(x)csc^{4}(cot(cot(x))) - 8cot(cot(x))cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) + 8cot(x)cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(cot(x)))csc^{6}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 6csc^{6}(x) - 42cot^{2}(x)csc^{4}(x) - 12cot^{4}(x)csc^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 2csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(x))cot(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))cot(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 2csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot(x)cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(cot(x))csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))cot(cot(x))csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) + 2csc^{6}(cot(x))csc^{6}(x)csc^{4}(cot(cot(x))) - 8cot(cot(x))cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) + 8cot(x)cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(cot(x)))csc^{6}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 6csc^{6}(x) - 42cot^{2}(x)csc^{4}(x) - 12cot^{4}(x)csc^{2}(x)\right)}{dx}\\=&2*-4csc^{4}(x)cot(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 2csc^{4}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) + 2csc^{4}(x)csc^{2}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 4*-csc^{2}(cot(x))*-csc^{2}(x)cot(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(x))cot(x)*-4csc^{4}(x)cot(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(x))cot(x)csc^{4}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) - 4cot(cot(x))cot(x)csc^{4}(x)csc^{2}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 4*-2cot(x)csc^{2}(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(x)csc^{2}(cot(x))*-2csc^{2}(x)cot(x)csc^{2}(cot(cot(x))) + 4cot^{2}(x)csc^{2}(cot(x))csc^{2}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 4*-csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)cot(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))*-csc^{2}(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))cot(x)*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))cot(x)csc^{4}(cot(x))*-4csc^{4}(x)cot(x)csc^{2}(cot(cot(x))) + 4cot(cot(cot(x)))cot(x)csc^{4}(cot(x))csc^{4}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 2*-6csc^{6}(x)cot(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) + 2csc^{6}(x)*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) + 2csc^{6}(x)csc^{4}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 8*-csc^{2}(x)cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 8cot(x)*-csc^{2}(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 8cot(x)cot(cot(x))*-4csc^{4}(x)cot(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 8cot(x)cot(cot(x))csc^{4}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) - 8cot(x)cot(cot(x))csc^{4}(x)csc^{2}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 4*-2cot(cot(x))csc^{2}(cot(x))*-csc^{2}(x)csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(cot(x))*-6csc^{6}(x)cot(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 4cot^{2}(cot(x))csc^{6}(x)*-2csc^{2}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(x))csc^{6}(x)csc^{2}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 4*-csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)cot(cot(x))csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))cot(cot(x))*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{6}(x)csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))cot(cot(x))csc^{4}(cot(x))*-6csc^{6}(x)cot(x)csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))cot(cot(x))csc^{4}(cot(x))csc^{6}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 2*-6csc^{6}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{6}(x)csc^{4}(cot(cot(x))) + 2csc^{6}(cot(x))*-6csc^{6}(x)cot(x)csc^{4}(cot(cot(x))) + 2csc^{6}(cot(x))csc^{6}(x)*-4csc^{4}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 8*-csc^{2}(cot(x))*-csc^{2}(x)cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot(cot(x))*-csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot(cot(x))cot(cot(cot(x)))*-6csc^{6}(x)cot(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot(cot(x))cot(cot(cot(x)))csc^{6}(x)*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{2}(cot(cot(x))) - 8cot(cot(x))cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 8*-csc^{2}(x)cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 8cot(x)*-csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 8cot(x)cot(cot(cot(x)))*-4csc^{4}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(cot(cot(x))) + 8cot(x)cot(cot(cot(x)))csc^{4}(cot(x))*-4csc^{4}(x)cot(x)csc^{2}(cot(cot(x))) + 8cot(x)cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) + 4*-2cot(cot(cot(x)))csc^{2}(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x)csc^{6}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(cot(x)))*-6csc^{6}(cot(x))cot(cot(x))*-csc^{2}(x)csc^{6}(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(cot(x)))csc^{6}(cot(x))*-6csc^{6}(x)cot(x)csc^{2}(cot(cot(x))) + 4cot^{2}(cot(cot(x)))csc^{6}(cot(x))csc^{6}(x)*-2csc^{2}(cot(cot(x)))cot(cot(cot(x)))*-csc^{2}(cot(x))*-csc^{2}(x) - 6*-6csc^{6}(x)cot(x) - 42*-2cot(x)csc^{2}(x)csc^{4}(x) - 42cot^{2}(x)*-4csc^{4}(x)cot(x) - 12*-4cot^{3}(x)csc^{2}(x)csc^{2}(x) - 12cot^{4}(x)*-2csc^{2}(x)cot(x)\\=&16cot(cot(x))csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 4cot(x)csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 4cot(x)csc^{6}(x)csc^{4}(cot(cot(x)))csc^{6}(cot(x)) - 20cot(x)csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 16cot(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 24cot(cot(x))cot^{2}(x)csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 32cot(x)cot^{2}(cot(x))csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 32cot(cot(cot(x)))cot(x)cot(cot(x))csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 12cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 8cot^{3}(x)csc^{2}(cot(x))csc^{2}(x)csc^{2}(cot(cot(x))) - 24cot(cot(cot(x)))cot^{2}(x)csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 4cot(cot(x))csc^{8}(x)csc^{4}(cot(cot(x)))csc^{6}(cot(x)) + 16cot(x)cot(cot(cot(x)))cot(cot(x))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 24cot^{2}(cot(cot(x)))cot(x)csc^{6}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) + 16cot(cot(x))csc^{8}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) + 8cot(cot(x))csc^{6}(cot(x))csc^{8}(x)csc^{4}(cot(cot(x))) - 4cot(cot(cot(x)))csc^{8}(x)csc^{6}(cot(x))csc^{2}(cot(cot(x))) + 32cot^{2}(x)cot(cot(x))csc^{4}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 16cot^{2}(cot(x))cot(x)csc^{6}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) + 16cot(cot(cot(x)))cot(cot(x))cot(x)csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 12cot(cot(cot(x)))csc^{6}(cot(x))csc^{8}(x)csc^{2}(cot(cot(x))) + 8cot^{3}(cot(x))csc^{8}(x)csc^{2}(cot(x))csc^{2}(cot(cot(x))) - 8cot(cot(cot(x)))cot^{2}(cot(x))csc^{4}(cot(x))csc^{8}(x)csc^{2}(cot(cot(x))) - 20cot(x)csc^{6}(cot(x))csc^{6}(x)csc^{4}(cot(cot(x))) - 16cot^{2}(cot(x))cot(cot(cot(x)))csc^{8}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) + 24cot^{2}(cot(cot(x)))cot(cot(x))csc^{6}(cot(x))csc^{8}(x)csc^{2}(cot(cot(x))) + 12cot(cot(x))csc^{8}(x)csc^{6}(cot(x))csc^{4}(cot(cot(x))) - 16cot(cot(cot(x)))csc^{8}(cot(x))csc^{8}(x)csc^{4}(cot(cot(x))) + 48cot(cot(x))cot(x)cot(cot(cot(x)))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 32cot(cot(cot(x)))cot^{2}(cot(x))csc^{8}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 4cot(cot(cot(x)))csc^{4}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) + 32cot(cot(cot(x)))cot(x)cot(cot(x))csc^{6}(x)csc^{4}(cot(x))csc^{2}(cot(cot(x))) - 32cot^{2}(x)cot(cot(cot(x)))csc^{4}(cot(x))csc^{4}(x)csc^{2}(cot(cot(x))) + 24cot(cot(x))cot^{2}(cot(cot(x)))csc^{8}(x)csc^{6}(cot(x))csc^{2}(cot(cot(x))) - 24cot(x)cot^{2}(cot(cot(x)))csc^{6}(cot(x))csc^{6}(x)csc^{2}(cot(cot(x))) - 8cot^{3}(cot(cot(x)))csc^{8}(cot(x))csc^{8}(x)csc^{2}(cot(cot(x))) + 120cot(x)csc^{6}(x) + 216cot^{3}(x)csc^{4}(x) + 24cot^{5}(x)csc^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[5/6]Find\ the\ 4th\ derivative\ of\ function\ sec(x)sec(x)sec(x) - sec(sec(sec(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sec^{3}(x) - sec(sec(sec(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sec^{3}(x) - sec(sec(sec(x)))\right)}{dx}\\=&3sec^{3}(x)tan(x) - sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)\\=&3tan(x)sec^{3}(x) - tan(sec(sec(x)))tan(x)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3tan(x)sec^{3}(x) - tan(sec(sec(x)))tan(x)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x))\right)}{dx}\\=&3sec^{2}(x)(1)sec^{3}(x) + 3tan(x)*3sec^{3}(x)tan(x) - sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(x)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))sec^{2}(x)(1)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan(x)sec^{2}(sec(x))(sec(x)tan(x))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan(x)tan(sec(x))sec(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan(x)tan(sec(x))sec(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - tan(sec(sec(x)))tan(x)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)\\=&3sec^{5}(x) + 9tan^{2}(x)sec^{3}(x) - tan^{2}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan(sec(sec(x)))tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 3sec^{5}(x) + 9tan^{2}(x)sec^{3}(x) - tan^{2}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan(sec(sec(x)))tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x))\right)}{dx}\\=&3*5sec^{5}(x)tan(x) + 9*2tan(x)sec^{2}(x)(1)sec^{3}(x) + 9tan^{2}(x)*3sec^{3}(x)tan(x) - 2tan(x)sec^{2}(x)(1)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan^{2}(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan^{2}(x)tan^{2}(sec(x))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec^{3}(sec(sec(x))) - tan^{2}(x)tan^{2}(sec(x))sec^{2}(sec(x))*2sec^{2}(x)tan(x)sec^{3}(sec(sec(x))) - tan^{2}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan(sec(x))*3sec^{3}(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(sec(x)))tan(sec(x))sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - tan(sec(sec(x)))tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan(sec(sec(x)))*2tan(x)sec^{2}(x)(1)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan(sec(sec(x)))tan^{2}(x)*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec(sec(sec(x))) - tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))*2sec^{2}(x)tan(x)sec(sec(sec(x))) - tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(x)sec^{2}(x)(1)tan(sec(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(x)sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(x)tan(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))*2tan(x)sec^{2}(x)(1)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{2}(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))*2tan(x)sec^{2}(x)(1)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x))tan(sec(x))sec(x)tan(x)\\=&33tan(x)sec^{5}(x) - tan(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 2tan(x)tan^{2}(sec(x))sec^{4}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - tan(x)tan^{2}(sec(x))sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{4}(x) - tan^{2}(sec(x))tan^{3}(x)sec^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{3}(x)tan(sec(sec(x)))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - tan^{3}(x)tan(sec(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan(x)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - 2tan^{3}(x)tan(sec(x))sec^{4}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) + 27tan^{3}(x)sec^{3}(x) - tan^{3}(sec(x))tan^{3}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{3}(x) - 2tan^{2}(sec(sec(x)))tan(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan^{2}(sec(x))tan(x)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))tan(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{3}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - tan(sec(x))tan(sec(sec(x)))tan^{3}(x)sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(x)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 2tan^{3}(sec(x))tan^{3}(x)sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{3}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x)))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 33tan(x)sec^{5}(x) - tan(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 2tan(x)tan^{2}(sec(x))sec^{4}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - tan(x)tan^{2}(sec(x))sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{4}(x) - tan^{2}(sec(x))tan^{3}(x)sec^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{3}(x)tan(sec(sec(x)))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - tan^{3}(x)tan(sec(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan(x)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - 2tan^{3}(x)tan(sec(x))sec^{4}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) + 27tan^{3}(x)sec^{3}(x) - tan^{3}(sec(x))tan^{3}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{3}(x) - 2tan^{2}(sec(sec(x)))tan(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan^{2}(sec(x))tan(x)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))tan(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{3}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - tan(sec(x))tan(sec(sec(x)))tan^{3}(x)sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(x)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 2tan^{3}(sec(x))tan^{3}(x)sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{3}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x)))\right)}{dx}\\=&33sec^{2}(x)(1)sec^{5}(x) + 33tan(x)*5sec^{5}(x)tan(x) - sec^{2}(x)(1)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - tan(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - tan(x)tan(sec(sec(x)))*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(x)sec(sec(sec(x))) - tan(x)tan(sec(sec(x)))sec^{3}(sec(x))*4sec^{4}(x)tan(x)sec(sec(sec(x))) - tan(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2sec^{2}(x)(1)tan^{2}(sec(x))sec^{4}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 2tan(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{4}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 2tan(x)tan^{2}(sec(x))*4sec^{4}(x)tan(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 2tan(x)tan^{2}(sec(x))sec^{4}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(sec(sec(x))) - 2tan(x)tan^{2}(sec(x))sec^{4}(x)sec^{2}(sec(x))*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - sec^{2}(x)(1)tan^{2}(sec(x))sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{4}(x) - tan(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{4}(x) - tan(x)tan^{2}(sec(x))*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(sec(x))sec^{4}(x) - tan(x)tan^{2}(sec(x))sec^{3}(sec(sec(x)))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(x) - tan(x)tan^{2}(sec(x))sec^{3}(sec(sec(x)))sec^{2}(sec(x))*4sec^{4}(x)tan(x) - 2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(x))tan^{3}(x)*2sec^{2}(x)tan(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(x))tan^{3}(x)sec^{2}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(sec(x)) - tan^{2}(sec(x))tan^{3}(x)sec^{2}(x)sec^{3}(sec(sec(x)))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 3tan^{2}(x)sec^{2}(x)(1)tan(sec(sec(x)))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x))) - tan^{3}(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x))) - tan^{3}(x)tan(sec(sec(x)))*2sec^{2}(x)tan(x)sec^{3}(sec(x))sec(sec(sec(x))) - tan^{3}(x)tan(sec(sec(x)))sec^{2}(x)*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(sec(x))) - tan^{3}(x)tan(sec(sec(x)))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))*3tan^{2}(x)sec^{2}(x)(1)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)tan^{3}(sec(x))*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)tan^{3}(sec(x))sec^{3}(sec(x))*3sec^{3}(x)tan(x)sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 3tan^{2}(x)sec^{2}(x)(1)tan(sec(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - tan^{3}(x)sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - tan^{3}(x)tan(sec(x))*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(sec(x))sec^{3}(x) - tan^{3}(x)tan(sec(x))sec^{3}(sec(sec(x)))*4sec^{4}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x) - tan^{3}(x)tan(sec(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))*3sec^{3}(x)tan(x) - 2sec^{2}(x)(1)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(x)tan(sec(sec(x)))*4sec^{4}(x)tan(x)sec^{3}(sec(x))sec(sec(sec(x))) - 2tan(x)tan(sec(sec(x)))sec^{4}(x)*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(sec(x))) - 2tan(x)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2sec^{2}(x)(1)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan(x)sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan(x)tan(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan(x)tan(sec(x))tan(sec(sec(x)))*3sec^{3}(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - 2tan(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - 2tan(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec^{2}(x)(1)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))*4sec^{4}(x)tan(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan(x)sec(sec(sec(x)))sec^{4}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - tan^{2}(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))sec^{2}(x)(1)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))*4sec^{4}(x)tan(x)sec(sec(x)) - tan^{2}(sec(x))tan(sec(sec(x)))tan(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(x)sec^{2}(x)(1)tan(sec(x))sec^{4}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)sec^{2}(sec(x))(sec(x)tan(x))sec^{4}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))*4sec^{4}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))sec^{4}(sec(x))*3sec^{3}(x)tan(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))sec^{4}(sec(x))sec^{3}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) + 27*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x) + 27tan^{3}(x)*3sec^{3}(x)tan(x) - 3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{3}(x) - tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{3}(x) - tan^{3}(sec(x))tan^{3}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(sec(x))sec^{3}(x) - tan^{3}(sec(x))tan^{3}(x)sec^{3}(sec(sec(x)))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x) - tan^{3}(sec(x))tan^{3}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))*3sec^{3}(x)tan(x) - 2*2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))sec^{2}(x)(1)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan(x)tan^{2}(sec(x))*4sec^{4}(x)tan(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - tan^{2}(sec(sec(x)))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - tan^{2}(sec(sec(x)))tan(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - tan^{2}(sec(sec(x)))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{4}(sec(x))sec^{3}(x) - tan^{2}(sec(sec(x)))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))*4sec^{4}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x) - tan^{2}(sec(sec(x)))tan(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{4}(sec(x))*3sec^{3}(x)tan(x) - 2*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(x)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{2}(sec(x))sec^{2}(x)(1)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{2}(sec(x))tan(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{2}(sec(x))tan(x)tan(sec(sec(x)))*4sec^{4}(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{2}(sec(x))tan(x)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - 2tan^{2}(sec(x))tan(x)tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 3sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))sec^{2}(x)(1)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))tan(x)sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))tan(x)tan(sec(x))*3sec^{3}(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(sec(x)))tan(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - 3tan(sec(sec(x)))tan(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(x)sec^{2}(x)(1)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))tan(sec(sec(x)))*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))*3sec^{3}(x)tan(x)sec(sec(sec(x))) - 2tan^{3}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))tan^{3}(x)sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(x)sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(x))tan(sec(sec(x)))*3tan^{2}(x)sec^{2}(x)(1)sec(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(x))tan(sec(sec(x)))tan^{3}(x)sec(x)tan(x)sec(sec(sec(x)))sec(sec(x)) - tan(sec(x))tan(sec(sec(x)))tan^{3}(x)sec(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(x)) - tan(sec(x))tan(sec(sec(x)))tan^{3}(x)sec(x)sec(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))*3tan^{2}(x)sec^{2}(x)(1)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan(sec(sec(x)))*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec(sec(x)) - tan(sec(sec(x)))tan^{2}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{2}(x)sec(sec(x))tan(sec(x))sec(x)tan(x) - 3*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 3tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)tan(sec(sec(x)))*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec^{3}(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))*3sec^{3}(x)tan(x)sec^{3}(sec(x)) - 3tan^{3}(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x) - 2*2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(x)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))*3tan^{2}(x)sec^{2}(x)(1)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{3}(x)sec^{2}(sec(x))(sec(x)tan(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{3}(x)tan(sec(x))*3sec^{3}(x)tan(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{3}(x)tan(sec(x))sec^{3}(x)*4sec^{4}(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{3}(x)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - 2tan(sec(sec(x)))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)sec^{3}(sec(x))*2sec^{2}(x)tan(x)sec(sec(sec(x))) - 2tan(sec(sec(x)))tan^{3}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 3tan^{2}(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - tan^{3}(sec(sec(x)))*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)*3sec^{3}(x)tan(x)sec(sec(sec(x)))sec^{3}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(x)sec^{2}(x)(1)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{3}(x)*2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec^{2}(sec(x)) - 2tan^{3}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2*2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))*3sec^{3}(x)tan(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec(sec(sec(x)))sec^{3}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(sec(x))tan^{3}(x)*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(sec(x))tan^{3}(x)sec^{2}(sec(x))*3sec^{3}(x)tan(x)sec^{3}(sec(sec(x))) - 2tan^{3}(sec(x))tan^{3}(x)sec^{2}(sec(x))sec^{3}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 3sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 3tan(sec(x))*3tan^{2}(x)sec^{2}(x)(1)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)tan(sec(sec(x)))*3sec^{3}(sec(x))tan(sec(x))sec(x)tan(x)sec^{3}(x)sec(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(x))*3sec^{3}(x)tan(x)sec(sec(sec(x))) - 3tan(sec(x))tan^{3}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(x)sec^{2}(x)(1)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan^{2}(sec(x))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan^{2}(sec(x))sec^{2}(sec(x))*2sec^{2}(x)tan(x)sec^{3}(sec(sec(x))) - 2tan^{3}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)*3sec^{3}(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x) - 2tan(sec(sec(x)))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)*3sec^{3}(x)tan(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{3}(x)sec^{3}(x)sec(sec(sec(x)))*2sec^{2}(sec(x))tan(sec(x))sec(x)tan(x) - 2*3tan^{2}(x)sec^{2}(x)(1)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 2tan^{3}(x)*2tan(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)sec^{2}(x)sec(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))*2sec^{2}(x)tan(x)sec(sec(x)) - 2tan^{3}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x))tan(sec(x))sec(x)tan(x) - 3tan^{2}(x)sec^{2}(x)(1)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - tan^{3}(x)*3tan^{2}(sec(x))sec^{2}(sec(x))(sec(x)tan(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - tan^{3}(x)tan^{3}(sec(x))sec^{2}(sec(sec(x)))(sec(sec(x))tan(sec(x))sec(x)tan(x))sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - tan^{3}(x)tan^{3}(sec(x))tan(sec(sec(x)))*3sec^{3}(x)tan(x)sec(sec(x))sec(sec(sec(x))) - tan^{3}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))tan(sec(x))sec(x)tan(x)sec(sec(sec(x))) - tan^{3}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x)))tan(sec(sec(x)))sec(sec(x))tan(sec(x))sec(x)tan(x)\\=&33sec^{7}(x) - 3tan^{4}(x)sec^{6}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 3tan(sec(sec(x)))sec^{6}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 6tan^{2}(x)tan(sec(x))sec^{5}(x)sec^{3}(sec(sec(x)))sec^{4}(sec(x)) - 2tan^{4}(x)tan^{4}(sec(x))sec^{4}(sec(x))sec^{4}(x)sec^{5}(sec(sec(x))) - 19tan^{2}(x)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - tan^{2}(x)tan(sec(x))tan^{2}(sec(sec(x)))sec(sec(sec(x)))sec^{4}(sec(x))sec^{5}(x) - 2tan^{2}(sec(x))sec^{6}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - tan^{4}(x)tan(sec(x))sec^{3}(x)sec^{3}(sec(sec(x)))sec^{4}(sec(x)) - tan^{4}(x)tan^{2}(sec(sec(x)))sec^{4}(x)sec^{6}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(x))tan^{2}(x)sec^{4}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 6tan(sec(sec(x)))tan^{2}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{5}(x)sec^{3}(sec(sec(x))) - tan^{2}(sec(x))sec^{6}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{3}(sec(x))tan^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{5}(x) - 3tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 2tan^{4}(x)tan(sec(x))sec^{3}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan^{4}(x)tan(sec(sec(x)))sec^{4}(x)sec^{5}(sec(x))sec(sec(sec(x))) - 6tan(sec(sec(x)))tan^{4}(x)tan^{2}(sec(x))sec^{5}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 4tan^{3}(sec(x))tan^{2}(x)sec^{5}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 6tan^{2}(x)tan(sec(x))sec^{4}(sec(x))sec^{5}(x)sec^{3}(sec(sec(x))) - tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - 3tan^{2}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - tan^{4}(x)tan(sec(x))tan^{2}(sec(sec(x)))sec(sec(sec(x)))sec^{3}(x)sec^{4}(sec(x)) - 9tan^{2}(sec(x))tan^{4}(x)sec^{4}(x)sec^{3}(sec(sec(x)))sec^{4}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{4}(x)sec^{6}(sec(x))sec^{4}(x)sec(sec(sec(x))) - tan^{2}(sec(x))tan^{4}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x))sec^{2}(x) - 2tan^{2}(x)tan(sec(x))tan^{2}(sec(sec(x)))sec(sec(sec(x)))sec^{5}(x)sec^{4}(sec(x)) - 6tan^{3}(sec(x))tan(sec(sec(x)))tan^{4}(x)sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 6tan^{2}(sec(sec(x)))tan^{4}(x)tan^{4}(sec(x))sec^{3}(sec(sec(x)))sec^{4}(x)sec^{4}(sec(x)) - 3tan^{2}(x)tan^{2}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 6tan^{2}(x)tan(sec(x))sec^{5}(x)sec^{4}(sec(x))sec^{3}(sec(sec(x))) - 2tan(sec(sec(x)))tan^{4}(x)tan^{3}(sec(x))sec^{3}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - tan^{4}(x)tan^{3}(sec(x))sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 3tan^{4}(x)tan(sec(sec(x)))sec^{5}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 6tan^{2}(x)tan(sec(sec(x)))tan^{3}(sec(x))sec^{5}(x)sec^{3}(sec(x))sec^{3}(sec(sec(x))) - 3tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec^{5}(sec(sec(x)))sec^{4}(sec(x)) - 2tan^{2}(sec(sec(x)))tan(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x) - 2tan(sec(x))tan(sec(sec(x)))sec^{5}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan(sec(x))tan^{2}(x)tan(sec(sec(x)))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 6tan(sec(sec(x)))tan^{2}(x)tan(sec(x))sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{2}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - 2tan(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - 2tan^{3}(sec(x))tan^{4}(x)sec^{3}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - tan^{2}(sec(x))tan^{2}(sec(sec(x)))sec^{6}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec^{5}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 4tan^{2}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - 4tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{5}(x)sec^{2}(sec(x)) - 3tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 2tan(sec(x))tan^{4}(x)tan^{2}(sec(sec(x)))sec^{4}(sec(x))sec^{3}(x)sec(sec(sec(x))) - tan(sec(sec(x)))tan^{2}(sec(x))sec^{6}(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec^{5}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 4tan^{2}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - 4tan^{2}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{5}(x)sec(sec(x))sec(sec(sec(x))) - 3tan^{2}(x)tan^{3}(sec(x))sec^{5}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 6tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{5}(x)sec(sec(sec(x))) - 9tan^{2}(x)tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 3tan^{2}(sec(sec(x)))tan^{4}(x)tan^{4}(sec(x))sec^{4}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) + 246tan^{2}(x)sec^{5}(x) - 9tan^{4}(x)tan^{2}(sec(x))sec^{4}(x)sec^{4}(sec(x))sec^{3}(sec(sec(x))) - 6tan^{2}(x)tan^{3}(sec(x))sec^{5}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 4tan^{3}(sec(x))tan(sec(sec(x)))tan^{4}(x)sec^{3}(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x) - 2tan(sec(sec(x)))tan^{4}(x)tan(sec(x))sec^{3}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 3tan(sec(sec(x)))tan^{2}(x)tan^{2}(sec(x))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 6tan(sec(sec(x)))tan^{4}(x)tan^{4}(sec(x))sec^{3}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{2}(sec(x))sec^{6}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 9tan^{4}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec^{5}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 8tan^{2}(sec(x))tan^{2}(sec(sec(x)))tan^{2}(x)sec^{4}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{5}(x)sec^{3}(sec(x)) - 4tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec^{5}(x)sec^{2}(sec(x))sec(sec(sec(x))) - 9tan^{2}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{5}(x)sec^{3}(sec(sec(x)))sec^{3}(sec(x)) - 6tan^{2}(x)tan^{2}(sec(sec(x)))tan(sec(x))sec^{5}(x)sec^{4}(sec(x))sec(sec(sec(x))) - tan^{3}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec^{4}(x)sec(sec(sec(x)))sec^{5}(sec(x)) - 4tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec^{4}(x)sec(sec(sec(x)))sec^{4}(sec(x)) - 3tan^{4}(x)tan^{2}(sec(sec(x)))tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{2}(x)tan(sec(x))sec^{5}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(x))tan(sec(sec(x)))sec^{6}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan^{3}(sec(sec(x)))tan^{4}(x)tan^{2}(sec(x))sec^{4}(x)sec^{5}(sec(x))sec(sec(sec(x))) - 8tan(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 2tan(sec(sec(x)))tan^{3}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{5}(x)sec(sec(x)) - 4tan(sec(x))tan^{2}(sec(sec(x)))tan^{4}(x)sec^{4}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 3tan(sec(sec(x)))tan(sec(x))sec^{5}(x)sec(sec(sec(x)))sec(sec(x)) - 15tan^{2}(x)tan(sec(x))tan(sec(sec(x)))sec^{5}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 9tan(sec(x))tan(sec(sec(x)))tan^{2}(x)sec^{3}(x)sec(sec(sec(x)))sec(sec(x)) - 3tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{2}(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - 3tan^{2}(sec(x))tan(sec(sec(x)))tan^{2}(x)sec(sec(sec(x)))sec^{4}(x)sec(sec(x)) - 3tan^{3}(sec(sec(x)))tan^{2}(x)tan^{3}(sec(x))sec^{5}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 9tan^{2}(sec(sec(x)))tan^{4}(x)tan^{2}(sec(x))sec^{4}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 6tan^{4}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 6tan(sec(sec(x)))tan^{4}(x)tan(sec(x))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{4}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{4}(sec(x))sec^{4}(x) - 9tan^{2}(sec(sec(x)))tan^{2}(x)tan^{3}(sec(x))sec^{5}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 3tan^{2}(sec(sec(x)))tan^{2}(x)tan(sec(x))sec^{5}(x)sec(sec(sec(x)))sec^{4}(sec(x)) - tan(sec(sec(x)))tan^{4}(x)tan(sec(x))sec(x)sec(sec(sec(x)))sec(sec(x)) - tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - tan^{4}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 3tan^{2}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(sec(x)))sec^{5}(sec(x)) - tan^{3}(sec(sec(x)))tan^{3}(sec(x))tan^{4}(x)sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 2tan^{2}(sec(x))tan^{2}(sec(sec(x)))tan^{4}(x)sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 4tan^{4}(x)tan(sec(x))tan(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 6tan^{2}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{5}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - tan^{2}(sec(sec(x)))tan^{3}(sec(x))tan^{4}(x)sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 2tan^{4}(x)tan(sec(sec(x)))tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - tan^{4}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - 3tan^{4}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 6tan^{2}(x)tan^{2}(sec(x))tan(sec(sec(x)))sec^{4}(x)sec(sec(sec(x)))sec(sec(x)) - 4tan(sec(x))tan^{2}(x)tan^{2}(sec(sec(x)))sec^{4}(sec(x))sec^{5}(x)sec(sec(sec(x))) - 9tan^{2}(sec(sec(x)))tan^{4}(x)tan^{4}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x)))sec^{4}(sec(x)) - 9tan(sec(sec(x)))tan^{3}(sec(x))tan^{4}(x)sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 9tan^{4}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x)) - 6tan^{3}(sec(x))tan^{2}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(sec(x))sec^{5}(x) - 2tan^{4}(x)tan(sec(sec(x)))sec^{2}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 6tan(sec(x))tan^{2}(sec(sec(x)))tan^{4}(x)sec^{3}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 8tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec^{4}(x)sec^{4}(sec(x))sec(sec(sec(x))) - 2tan^{3}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(x)sec^{5}(sec(x)) - 5tan^{4}(x)tan(sec(x))sec^{3}(x)sec^{4}(sec(x))sec^{3}(sec(sec(x))) - 18tan^{2}(x)tan^{2}(sec(x))sec^{4}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 6tan(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 4tan(sec(sec(x)))tan^{4}(x)sec^{3}(sec(x))sec^{2}(x)sec(sec(sec(x))) - 6tan(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec^{3}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 6tan^{2}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{4}(x)sec^{5}(sec(x)) - 6tan(sec(x))tan(sec(sec(x)))tan^{2}(x)sec^{5}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 4tan^{2}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 3tan^{4}(x)tan^{3}(sec(sec(x)))tan^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - tan^{4}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(x)sec^{4}(sec(x)) - 3tan^{3}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 3tan^{4}(x)tan^{4}(sec(x))tan(sec(sec(x)))sec^{4}(x)sec^{3}(sec(sec(x)))sec^{3}(sec(x)) - 2tan^{3}(sec(sec(x)))tan^{4}(x)tan^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 4tan^{2}(sec(x))tan^{4}(x)tan^{2}(sec(sec(x)))sec(sec(sec(x)))sec^{2}(x)sec^{2}(sec(x)) - 4tan^{4}(x)tan^{3}(sec(x))tan^{2}(sec(sec(x)))sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 3tan^{3}(sec(x))tan^{2}(x)tan(sec(sec(x)))sec^{5}(x)sec^{3}(sec(sec(x)))sec^{3}(sec(x)) - 5tan^{3}(sec(x))tan^{4}(x)sec^{3}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 2tan^{3}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec(sec(sec(x)))sec^{3}(sec(x)) - 6tan^{4}(x)tan^{2}(sec(sec(x)))tan^{3}(sec(x))sec(sec(sec(x)))sec^{3}(x)sec^{2}(sec(x)) - 4tan^{2}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x)) - 4tan^{4}(sec(x))tan^{4}(x)sec^{2}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 10tan^{3}(sec(x))tan^{4}(x)sec^{2}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 6tan^{4}(x)tan^{4}(sec(x))tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x)) - 10tan^{4}(x)tan(sec(x))sec^{4}(sec(x))sec^{3}(x)sec^{3}(sec(sec(x))) - 3tan(sec(x))tan(sec(sec(x)))tan^{4}(x)sec^{3}(x)sec^{3}(sec(x))sec(sec(sec(x))) - 9tan^{2}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(x))sec^{4}(x)sec(sec(sec(x))) - 9tan(sec(sec(x)))tan(sec(x))tan^{4}(x)sec^{3}(sec(x))sec^{3}(x)sec(sec(sec(x))) - 3tan^{2}(sec(sec(x)))tan^{2}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(sec(x))sec^{4}(x) + 81tan^{4}(x)sec^{3}(x) - 4tan^{4}(x)tan^{2}(sec(x))sec^{2}(sec(x))sec^{2}(x)sec^{3}(sec(sec(x))) - 6tan^{3}(sec(x))tan^{4}(x)tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 3tan^{4}(x)tan^{3}(sec(x))tan(sec(sec(x)))sec^{3}(sec(sec(x)))sec^{3}(x)sec^{3}(sec(x)) - 3tan(sec(x))tan(sec(sec(x)))tan^{2}(x)sec^{3}(sec(x))sec^{5}(x)sec(sec(sec(x))) - 3tan^{4}(x)tan^{2}(sec(sec(x)))tan^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - tan^{3}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec(sec(sec(x)))sec^{4}(x)sec^{3}(sec(x)) - 2tan^{2}(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec^{2}(sec(x))sec(sec(sec(x))) - 8tan^{2}(sec(x))tan^{4}(x)sec^{4}(sec(x))sec^{4}(x)sec^{3}(sec(sec(x))) - 2tan^{2}(sec(sec(x)))tan^{4}(x)tan^{3}(sec(x))sec^{3}(x)sec(sec(sec(x)))sec^{2}(sec(x)) - 4tan(sec(sec(x)))tan^{4}(x)tan^{2}(sec(x))sec(sec(sec(x)))sec^{2}(x)sec(sec(x)) - 2tan(sec(sec(x)))tan^{3}(sec(x))tan^{4}(x)sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - 2tan^{2}(sec(x))tan^{4}(x)sec^{2}(x)sec^{3}(sec(sec(x)))sec^{2}(sec(x)) - 4tan^{3}(sec(x))tan^{2}(x)sec^{5}(x)sec^{2}(sec(x))sec^{3}(sec(sec(x))) - 3tan(sec(sec(x)))tan^{4}(x)tan^{3}(sec(x))sec^{3}(x)sec(sec(x))sec(sec(sec(x))) - tan(sec(sec(x)))tan^{4}(sec(x))tan^{4}(x)sec^{4}(x)sec(sec(x))sec(sec(sec(x))) - tan^{2}(sec(sec(x)))tan^{4}(x)tan^{4}(sec(x))sec(sec(sec(x)))sec^{4}(x)sec^{2}(sec(x))\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[6/6]Find\ the\ 4th\ derivative\ of\ function\ csc(x)csc(x)csc(x) - csc(csc(csc(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = csc^{3}(x) - csc(csc(csc(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( csc^{3}(x) - csc(csc(csc(x)))\right)}{dx}\\=&-3csc^{3}(x)cot(x) - -csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)\\=&-3cot(x)csc^{3}(x) + cot(csc(x))cot(x)cot(csc(csc(x)))csc(x)csc(csc(x))csc(csc(csc(x)))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3cot(x)csc^{3}(x) + cot(csc(x))cot(x)cot(csc(csc(x)))csc(x)csc(csc(x))csc(csc(csc(x)))\right)}{dx}\\=&-3*-csc^{2}(x)csc^{3}(x) - 3cot(x)*-3csc^{3}(x)cot(x) + -csc^{2}(csc(x))*-csc(x)cot(x)cot(x)cot(csc(csc(x)))csc(x)csc(csc(x))csc(csc(csc(x))) + cot(csc(x))*-csc^{2}(x)cot(csc(csc(x)))csc(x)csc(csc(x))csc(csc(csc(x))) + cot(csc(x))cot(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(x)csc(csc(x))csc(csc(csc(x))) + cot(csc(x))cot(x)cot(csc(csc(x)))*-csc(x)cot(x)csc(csc(x))csc(csc(csc(x))) + cot(csc(x))cot(x)cot(csc(csc(x)))csc(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + cot(csc(x))cot(x)cot(csc(csc(x)))csc(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)\\=&3csc^{5}(x) - cot(csc(x))cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) + 9cot^{2}(x)csc^{3}(x) - cot^{2}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))cot^{2}(x)csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 3csc^{5}(x) - cot(csc(x))cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) + 9cot^{2}(x)csc^{3}(x) - cot^{2}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))cot^{2}(x)csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x))\right)}{dx}\\=&3*-5csc^{5}(x)cot(x) - -csc^{2}(csc(x))*-csc(x)cot(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(x))*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(x))cot(csc(csc(x)))*-3csc^{3}(x)cot(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(x))cot(csc(csc(x)))csc^{3}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - cot(csc(x))cot(csc(csc(x)))csc^{3}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -2cot(x)csc^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) + cot^{2}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) + cot^{2}(x)cot(csc(csc(x)))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(csc(x))) + cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))*-2csc^{2}(x)cot(x)csc(csc(csc(x))) + cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 9*-2cot(x)csc^{2}(x)csc^{3}(x) + 9cot^{2}(x)*-3csc^{3}(x)cot(x) - -2cot(x)csc^{2}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{2}(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{2}(x)cot^{2}(csc(x))*-2csc^{2}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{2}(x)cot^{2}(csc(x))csc^{2}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) - cot^{2}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot(csc(x))cot^{2}(x)csc(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))*-csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(x)csc(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))*-2cot(x)csc^{2}(x)csc(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))cot^{2}(x)*-csc(x)cot(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))cot^{2}(x)csc(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - cot(csc(csc(x)))cot(csc(x))cot^{2}(x)csc(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))*-2cot(x)csc^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))*-2csc^{2}(x)cot(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{2}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{2}(csc(x))cot^{2}(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))*-2cot(x)csc^{2}(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)*-2csc^{2}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)csc^{2}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)csc^{2}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)\\=& - 33cot(x)csc^{5}(x) - 3cot(x)cot(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)cot(csc(x))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) - cot(csc(x))cot^{3}(x)csc^{3}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(x))cot^{2}(csc(csc(x)))cot^{3}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) + 2cot(x)cot^{2}(csc(x))csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 27cot^{3}(x)csc^{3}(x) - 2cot(csc(x))cot^{3}(x)csc^{4}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) + 2cot^{2}(csc(csc(x)))cot(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 2cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 3cot^{3}(csc(x))cot(csc(csc(x)))cot^{3}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x)csc^{2}(csc(x)) - cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))cot(csc(x))csc(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot(csc(csc(x)))cot^{2}(csc(x))cot(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) - cot^{3}(x)cot^{3}(csc(x))csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{3}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 3cot(csc(csc(x)))cot^{3}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x)))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 33cot(x)csc^{5}(x) - 3cot(x)cot(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)cot(csc(x))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) - cot(csc(x))cot^{3}(x)csc^{3}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(x))cot^{2}(csc(csc(x)))cot^{3}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) + 2cot(x)cot^{2}(csc(x))csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 27cot^{3}(x)csc^{3}(x) - 2cot(csc(x))cot^{3}(x)csc^{4}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) + 2cot^{2}(csc(csc(x)))cot(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 2cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 3cot^{3}(csc(x))cot(csc(csc(x)))cot^{3}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x)csc^{2}(csc(x)) - cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))cot(csc(x))csc(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot(csc(csc(x)))cot^{2}(csc(x))cot(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) - cot^{3}(x)cot^{3}(csc(x))csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{3}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 3cot(csc(csc(x)))cot^{3}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x)))\right)}{dx}\\=& - 33*-csc^{2}(x)csc^{5}(x) - 33cot(x)*-5csc^{5}(x)cot(x) - 3*-csc^{2}(x)cot(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 3cot(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{4}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 3cot(x)cot(csc(csc(x)))*-4csc^{4}(x)cot(x)csc^{3}(csc(x))csc(csc(csc(x))) - 3cot(x)cot(csc(csc(x)))csc^{4}(x)*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - 3cot(x)cot(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + cot^{2}(csc(x))*-csc^{2}(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + cot^{2}(csc(x))cot(x)*-4csc^{4}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + cot^{2}(csc(x))cot(x)csc^{4}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) + cot^{2}(csc(x))cot(x)csc^{4}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot(x)cot(csc(x))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 2cot(csc(csc(x)))*-csc^{2}(x)cot(csc(x))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)*-csc^{2}(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)cot(csc(x))*-3csc^{3}(x)cot(x)csc(csc(x))csc(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)cot(csc(x))csc^{3}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + 2cot(csc(csc(x)))cot(x)cot(csc(x))csc^{3}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-3cot^{2}(x)csc^{2}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)*-csc^{2}(csc(x))*-csc(x)cot(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))cot(csc(csc(x)))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))*-3csc^{3}(x)cot(x)csc(csc(csc(x))) + 2cot^{3}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) + 2cot^{3}(csc(x))*-3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) + 2cot^{3}(csc(x))cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) + 2cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc^{3}(csc(x)) + 2cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))*-3csc^{3}(x)cot(x)csc^{3}(csc(x)) + 2cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{3}(x)*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x) - -csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{3}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - cot(csc(x))*-3cot^{2}(x)csc^{2}(x)csc^{3}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - cot(csc(x))cot^{3}(x)*-3csc^{3}(x)cot(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - cot(csc(x))cot^{3}(x)csc^{3}(x)*-4csc^{4}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) - cot(csc(x))cot^{3}(x)csc^{3}(x)csc^{4}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(csc(x))*-3cot^{2}(x)csc^{2}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))*-3csc^{3}(x)cot(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{3}(x)*-4csc^{4}(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-csc^{2}(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))cot(csc(csc(x)))*-4csc^{4}(x)cot(x)csc(csc(x))csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - 2cot(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(csc(csc(x)))cot^{3}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) - cot(csc(x))*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) - cot(csc(x))cot^{2}(csc(csc(x)))*-3cot^{2}(x)csc^{2}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) - cot(csc(x))cot^{2}(csc(csc(x)))cot^{3}(x)*-4csc^{4}(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x)))csc^{3}(x) - cot(csc(x))cot^{2}(csc(csc(x)))cot^{3}(x)csc^{4}(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x) - cot(csc(x))cot^{2}(csc(csc(x)))cot^{3}(x)csc^{4}(csc(x))csc(csc(csc(x)))*-3csc^{3}(x)cot(x) + 2*-csc^{2}(x)cot^{2}(csc(x))csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(x)cot^{2}(csc(x))*-4csc^{4}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(x)cot^{2}(csc(x))csc^{4}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) + 2cot(x)cot^{2}(csc(x))csc^{4}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 27*-3cot^{2}(x)csc^{2}(x)csc^{3}(x) - 27cot^{3}(x)*-3csc^{3}(x)cot(x) - 2*-csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{4}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) - 2cot(csc(x))*-3cot^{2}(x)csc^{2}(x)csc^{4}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)*-4csc^{4}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc^{3}(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)csc^{4}(csc(x))*-3csc^{3}(x)cot(x)csc^{3}(csc(csc(x))) - 2cot(csc(x))cot^{3}(x)csc^{4}(csc(x))csc^{3}(x)*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{2}(csc(csc(x)))*-csc^{2}(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{2}(csc(csc(x)))cot(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{2}(csc(csc(x)))cot(x)cot^{2}(csc(x))*-4csc^{4}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{2}(csc(csc(x)))cot(x)cot^{2}(csc(x))csc^{4}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) + 2cot^{2}(csc(csc(x)))cot(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 2cot^{3}(csc(x))*-3cot^{2}(x)csc^{2}(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)*-3csc^{3}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 3*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot(csc(csc(x)))cot^{3}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 3cot^{3}(csc(x))*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 3cot^{3}(csc(x))cot(csc(csc(x)))*-3cot^{2}(x)csc^{2}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 3cot^{3}(csc(x))cot(csc(csc(x)))cot^{3}(x)*-3csc^{3}(x)cot(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 3cot^{3}(csc(x))cot(csc(csc(x)))cot^{3}(x)csc^{3}(x)*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(x)) + 3cot^{3}(csc(x))cot(csc(csc(x)))cot^{3}(x)csc^{3}(x)csc^{3}(csc(csc(x)))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x) + -3cot^{2}(x)csc^{2}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x)csc^{2}(csc(x)) + cot^{3}(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x)))csc^{2}(x)csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))*-2csc^{2}(x)cot(x)csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) - -3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc^{3}(csc(x))csc(csc(csc(x))) - cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc^{3}(csc(x))csc(csc(csc(x))) - cot^{3}(x)cot(csc(csc(x)))*-2csc^{2}(x)cot(x)csc^{3}(csc(x))csc(csc(csc(x))) - cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc^{3}(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 3*-csc^{2}(csc(x))*-csc(x)cot(x)cot(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 3cot(csc(x))*-csc^{2}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot(x)cot(csc(csc(x)))*-3csc^{3}(x)cot(x)csc(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot(x)cot(csc(csc(x)))csc^{3}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + 3cot(csc(x))cot(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))cot(csc(x))csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot(csc(x))csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))*-csc^{2}(csc(x))*-csc(x)cot(x)csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))cot(csc(x))*-csc(x)cot(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))cot(csc(x))csc(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + cot^{3}(x)cot(csc(csc(x)))cot(csc(x))csc(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))*-3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)cot(csc(csc(x)))*-2csc^{2}(x)cot(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - cot^{2}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{2}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -3cot^{2}(x)csc^{2}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))*-2csc^{2}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{2}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) + cot^{3}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) - -csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{2}(csc(x))cot(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot^{2}(csc(x))*-csc^{2}(x)csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot^{2}(csc(x))cot(x)*-4csc^{4}(x)cot(x)csc(csc(x))csc(csc(csc(x))) - cot(csc(csc(x)))cot^{2}(csc(x))cot(x)csc^{4}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - cot(csc(csc(x)))cot^{2}(csc(x))cot(x)csc^{4}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) - 2cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) - 2cot^{3}(x)cot(csc(csc(x)))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(csc(x))) - 2cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(x))*-2csc^{2}(x)cot(x)csc(csc(csc(x))) - 2cot^{3}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -3cot^{2}(x)csc^{2}(x)cot^{3}(csc(x))csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{3}(x)*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{3}(x)cot^{3}(csc(x))*-3csc^{3}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - cot^{3}(x)cot^{3}(csc(x))csc^{3}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) - cot^{3}(x)cot^{3}(csc(x))csc^{3}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{2}(csc(x))cot^{3}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(csc(csc(x)))*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))*-3cot^{2}(x)csc^{2}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{3}(x)*-2csc^{2}(x)cot(x)csc(csc(x))csc(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{3}(x)csc^{2}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) - 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{3}(x)csc^{2}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + -3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))*-3cot^{2}(x)csc^{2}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))*-3csc^{3}(x)cot(x)csc(csc(x))csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(x)*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc(csc(csc(x))) + cot^{3}(csc(x))cot^{3}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - -2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))*-3cot^{2}(x)csc^{2}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{3}(x)*-3csc^{3}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) - cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{3}(x)csc^{3}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) + -2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{2}(csc(csc(x)))cot(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))*-csc^{2}(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot(x)*-4csc^{4}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot(x)csc^{4}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) + cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot(x)csc^{4}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) + 3*-csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{3}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 3cot(csc(csc(x)))*-3cot^{2}(x)csc^{2}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 3cot(csc(csc(x)))cot^{3}(x)*-csc^{2}(csc(x))*-csc(x)cot(x)csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 3cot(csc(csc(x)))cot^{3}(x)cot(csc(x))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(csc(x))) + 3cot(csc(csc(x)))cot^{3}(x)cot(csc(x))csc^{3}(csc(x))*-3csc^{3}(x)cot(x)csc(csc(csc(x))) + 3cot(csc(csc(x)))cot^{3}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-3cot^{2}(x)csc^{2}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{3}(x)*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(x))*-2csc^{2}(x)cot(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(x))csc^{2}(x)*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(csc(x))) + 2cot^{3}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))*-3csc^{3}(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) + 2*-3cot^{2}(x)csc^{2}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{3}(x)*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{3}(x)cot^{2}(csc(csc(x)))*-2cot(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{3}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))*-2csc^{2}(x)cot(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{3}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x)) + 2cot^{3}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x) + -3cot^{2}(x)csc^{2}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + cot^{3}(x)*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + cot^{3}(x)cot^{3}(csc(x))*-3cot^{2}(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + cot^{3}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))*-3csc^{3}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(csc(x))) + cot^{3}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))*-3csc^{3}(x)cot(x)csc(csc(csc(x))) + cot^{3}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x) - 2*-3cot^{2}(csc(x))csc^{2}(csc(x))*-csc(x)cot(x)cot^{3}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))*-3cot^{2}(x)csc^{2}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)*-2cot(csc(csc(x)))csc^{2}(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))*-2csc^{2}(csc(x))cot(csc(x))*-csc(x)cot(x)csc^{3}(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))*-3csc^{3}(x)cot(x)csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{3}(x)*-csc(csc(csc(x)))cot(csc(csc(x)))*-csc(csc(x))cot(csc(x))*-csc(x)cot(x)\\=&33csc^{7}(x) - 2cot(csc(csc(x)))cot(csc(x))csc^{5}(x)csc(csc(x))csc(csc(csc(x))) + 3cot(csc(csc(x)))csc^{6}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 3cot(csc(x))cot^{2}(x)csc^{5}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 6cot^{2}(x)cot(csc(x))cot(csc(csc(x)))csc^{5}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 15cot^{4}(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{5}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) + 4cot^{2}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{4}(x)csc^{5}(csc(x))csc^{3}(csc(csc(x))) + 11cot^{2}(x)cot(csc(x))csc^{5}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 3cot^{2}(csc(x))csc^{6}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 6cot^{2}(x)cot^{3}(csc(x))cot(csc(csc(x)))csc^{5}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) - 6cot(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{5}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 8cot^{2}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{5}(csc(x))csc^{3}(csc(csc(x)))csc^{4}(x) - 2cot^{2}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{4}(x)csc^{2}(csc(x)) + 2cot(csc(csc(x)))cot^{2}(x)csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 6cot(csc(x))cot(csc(csc(x)))cot^{2}(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + 5cot^{2}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 10cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot^{2}(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 6cot^{2}(x)cot(csc(x))cot^{2}(csc(csc(x)))csc^{5}(x)csc^{4}(csc(x))csc(csc(csc(x))) + 2cot^{4}(x)cot(csc(csc(x)))csc^{4}(x)csc^{5}(csc(x))csc(csc(csc(x))) - 2cot^{2}(csc(x))cot^{4}(x)csc^{4}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) + 6cot^{2}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 12cot(csc(csc(x)))cot^{4}(x)cot(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 2cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{4}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{4}(x) + 4cot^{2}(x)cot^{2}(csc(csc(x)))cot(csc(x))csc^{4}(csc(x))csc^{5}(x)csc(csc(csc(x))) + 3cot(csc(x))cot^{2}(x)cot^{2}(csc(csc(x)))csc^{5}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot^{4}(x)cot^{4}(csc(x))csc^{4}(x)csc^{4}(csc(x))csc^{5}(csc(csc(x))) - 6cot^{2}(csc(csc(x)))cot^{4}(csc(x))cot^{4}(x)csc^{4}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 6cot(csc(csc(x)))cot^{3}(csc(x))cot^{4}(x)csc^{3}(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x)) + 6cot^{4}(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) - 3cot^{4}(x)csc^{4}(x)csc^{6}(csc(x))csc^{3}(csc(csc(x))) + 2cot^{2}(csc(x))cot(csc(csc(x)))csc^{6}(x)csc(csc(x))csc(csc(csc(x))) - 9cot^{3}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{5}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) - 4cot^{3}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{5}(x)csc^{3}(csc(x)) - 3cot^{4}(x)cot^{2}(csc(csc(x)))csc^{6}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 3cot^{2}(x)cot(csc(csc(x)))cot(csc(x))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - 5cot^{3}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{3}(x)csc^{3}(csc(x))csc^{3}(csc(csc(x))) + 6cot^{2}(csc(csc(x)))cot(csc(x))cot^{4}(x)csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 11cot^{2}(csc(x))cot^{4}(x)cot^{2}(csc(csc(x)))csc^{4}(x)csc^{4}(csc(x))csc(csc(csc(x))) + 2cot^{3}(csc(csc(x)))cot^{2}(csc(x))cot^{4}(x)csc^{4}(x)csc(csc(csc(x)))csc^{5}(csc(x)) - 2cot^{4}(x)cot(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 6cot^{3}(csc(x))cot^{2}(x)csc^{5}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 14cot(csc(csc(x)))cot^{2}(x)cot^{2}(csc(x))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 2cot^{3}(csc(x))cot(csc(csc(x)))cot^{2}(x)csc^{5}(x)csc(csc(x))csc(csc(csc(x))) + 2cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{2}(x)csc^{5}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot^{4}(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{3}(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x)) + 3cot^{2}(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - 4cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{4}(csc(x))csc^{4}(x)csc(csc(csc(x))) + cot^{4}(x)cot^{2}(csc(x))cot^{3}(csc(csc(x)))csc^{5}(csc(x))csc^{4}(x)csc(csc(csc(x))) + 3cot^{4}(x)cot(csc(x))cot^{2}(csc(csc(x)))csc^{3}(x)csc(csc(csc(x)))csc^{4}(csc(x)) + 4cot(csc(x))cot^{2}(x)csc^{4}(csc(x))csc^{5}(x)csc^{3}(csc(csc(x))) - 7cot^{2}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot(csc(x))cot^{4}(x)cot^{2}(csc(csc(x)))csc^{3}(x)csc^{4}(csc(x))csc(csc(csc(x))) - 2cot^{3}(csc(x))cot(csc(csc(x)))cot^{2}(x)csc^{3}(csc(x))csc^{3}(csc(csc(x)))csc^{5}(x) + 246cot^{2}(x)csc^{5}(x) - 2cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{6}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 11cot^{2}(x)cot^{3}(csc(x))csc^{5}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 4cot^{4}(x)cot(csc(csc(x)))cot^{3}(csc(x))csc^{3}(csc(x))csc^{3}(csc(csc(x)))csc^{3}(x) - 3cot^{4}(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{4}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 3cot^{2}(x)cot^{2}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x)))csc^{2}(csc(x)) - 4cot(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{3}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{3}(csc(csc(x)))cot^{2}(x)csc^{3}(csc(x))csc^{5}(x)csc(csc(csc(x))) + 4cot^{3}(csc(x))cot^{2}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{5}(x)csc(csc(csc(x))) - 10cot^{4}(x)cot^{2}(csc(x))csc^{4}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) + 21cot^{2}(x)cot(csc(csc(x)))csc^{4}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 3cot^{2}(x)cot^{3}(csc(x))cot(csc(csc(x)))csc^{5}(x)csc(csc(x))csc(csc(csc(x))) + 3cot^{4}(x)cot^{2}(csc(x))cot(csc(csc(x)))csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) + 4cot^{4}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{4}(x)csc^{3}(csc(x))csc^{3}(csc(csc(x))) - 3cot^{4}(csc(x))cot^{4}(x)csc^{4}(csc(x))csc^{5}(csc(csc(x)))csc^{4}(x) + 3cot^{2}(csc(csc(x)))cot^{2}(x)cot^{3}(csc(x))csc^{5}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 9cot^{4}(x)cot^{3}(csc(x))cot(csc(csc(x)))csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) - 9cot^{4}(x)cot^{4}(csc(x))cot^{2}(csc(csc(x)))csc^{4}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) + 9cot^{4}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{3}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) - 3cot(csc(x))cot(csc(csc(x)))csc^{5}(x)csc(csc(x))csc(csc(csc(x))) + 12cot(csc(x))cot^{4}(x)csc^{4}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) - 9cot^{2}(x)cot(csc(csc(x)))cot(csc(x))csc^{5}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 2cot^{2}(x)cot(csc(x))cot^{2}(csc(csc(x)))csc^{4}(csc(x))csc^{5}(x)csc(csc(csc(x))) + cot(csc(csc(x)))cot^{2}(csc(x))csc^{6}(x)csc(csc(x))csc(csc(csc(x))) + 6cot(csc(x))cot^{4}(x)csc^{3}(x)csc^{4}(csc(x))csc^{3}(csc(csc(x))) - 6cot^{2}(x)cot^{2}(csc(csc(x)))cot^{2}(csc(x))csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 4cot^{2}(csc(csc(x)))cot^{4}(x)cot(csc(x))csc^{4}(csc(x))csc^{3}(x)csc(csc(csc(x))) + cot(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{3}(x)csc(csc(csc(x)))csc^{4}(csc(x)) + 3cot^{2}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 17cot^{2}(x)cot^{2}(csc(x))csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 9cot(csc(csc(x)))cot(csc(x))cot^{2}(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) - 3cot^{2}(csc(csc(x)))cot^{2}(csc(x))cot^{2}(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 3cot^{2}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{5}(x)csc^{3}(csc(x))csc(csc(csc(x))) - cot^{2}(csc(x))cot^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x) + 5cot^{4}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{2}(x)csc(csc(csc(x))) - cot(csc(x))cot^{4}(x)cot(csc(csc(x)))csc(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - 5cot^{2}(csc(x))cot^{4}(x)cot^{2}(csc(csc(x)))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 3cot^{2}(csc(x))cot^{4}(x)cot^{3}(csc(csc(x)))csc^{4}(x)csc^{5}(csc(x))csc(csc(csc(x))) + 6cot^{2}(x)cot^{3}(csc(x))cot^{2}(csc(csc(x)))csc^{5}(x)csc^{2}(csc(x))csc(csc(csc(x))) + 4cot^{4}(x)cot^{3}(csc(x))csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 2cot(csc(csc(x)))cot^{2}(csc(x))cot^{4}(x)csc^{2}(x)csc(csc(x))csc(csc(csc(x))) - 3cot^{3}(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{4}(x)csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 6cot^{4}(x)cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{4}(csc(x))csc^{4}(x)csc(csc(csc(x))) + 3cot(csc(x))cot^{2}(csc(csc(x)))cot^{2}(x)csc^{5}(x)csc(csc(csc(x)))csc^{4}(csc(x)) - 2cot^{2}(csc(csc(x)))cot^{4}(x)cot^{2}(csc(x))csc^{2}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{3}(csc(csc(x)))cot^{3}(csc(x))cot^{4}(x)csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 6cot^{3}(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x))) + cot^{2}(x)cot^{3}(csc(x))csc^{3}(csc(csc(x)))csc^{5}(x)csc^{2}(csc(x)) - 8cot^{4}(x)cot^{2}(csc(x))csc^{4}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) + 4cot^{2}(x)cot(csc(csc(x)))cot^{2}(csc(x))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot^{3}(csc(x))cot^{2}(x)cot(csc(csc(x)))csc^{5}(x)csc(csc(x))csc(csc(csc(x))) + cot^{2}(x)cot^{3}(csc(x))cot^{2}(csc(csc(x)))csc^{5}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - cot^{2}(csc(x))cot^{2}(csc(csc(x)))csc^{6}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + 2cot(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{3}(x) - 3cot^{2}(csc(x))cot^{4}(x)csc^{4}(csc(x))csc^{4}(x)csc^{3}(csc(csc(x))) - 2cot^{4}(csc(x))cot^{4}(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 9cot^{4}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{4}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 2cot^{4}(x)cot^{3}(csc(x))csc^{3}(csc(csc(x)))csc^{3}(x)csc^{2}(csc(x)) - 9cot(csc(csc(x)))cot^{2}(x)cot(csc(x))csc^{5}(x)csc^{3}(csc(x))csc(csc(csc(x))) + 4cot^{4}(x)cot(csc(csc(x)))cot^{2}(csc(x))csc^{2}(x)csc(csc(x))csc(csc(csc(x))) + 2cot^{4}(x)cot^{3}(csc(x))cot^{2}(csc(csc(x)))csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 5cot^{4}(x)cot^{4}(csc(x))csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 10cot^{3}(csc(x))cot^{4}(x)csc^{3}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 3cot(csc(csc(x)))cot^{3}(csc(x))cot^{4}(x)csc^{3}(x)csc(csc(x))csc(csc(csc(x))) + cot^{4}(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{4}(x)csc(csc(x))csc(csc(csc(x))) - cot^{2}(csc(csc(x)))cot^{4}(csc(x))cot^{4}(x)csc^{4}(x)csc(csc(csc(x)))csc^{2}(csc(x)) - 9cot^{3}(csc(x))cot(csc(csc(x)))cot^{2}(x)csc^{5}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 3cot^{4}(x)cot^{2}(csc(csc(x)))cot^{3}(csc(x))csc^{3}(x)csc(csc(csc(x)))csc^{2}(csc(x)) + cot^{4}(x)cot^{4}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 6cot^{4}(csc(x))cot^{4}(x)cot^{2}(csc(csc(x)))csc^{2}(csc(x))csc^{4}(x)csc(csc(csc(x))) + 2cot^{3}(csc(x))cot^{4}(x)csc^{2}(csc(x))csc^{3}(x)csc^{3}(csc(csc(x))) + 81cot^{4}(x)csc^{3}(x) - cot^{2}(x)cot^{3}(csc(x))cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{5}(x)csc(csc(csc(x))) + 2cot^{3}(csc(x))cot^{2}(csc(csc(x)))cot^{2}(x)csc^{2}(csc(x))csc^{5}(x)csc(csc(csc(x))) - 3cot^{4}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{4}(x)csc^{4}(csc(x)) - 2cot^{4}(x)cot^{2}(csc(x))csc^{3}(csc(csc(x)))csc^{2}(x)csc^{2}(csc(x)) + 3cot(csc(csc(x)))cot^{4}(x)csc^{5}(csc(x))csc^{4}(x)csc(csc(csc(x))) + 9cot^{2}(csc(x))cot^{4}(x)cot(csc(csc(x)))csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 9cot(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) - 3cot^{2}(csc(x))cot^{2}(csc(csc(x)))cot^{4}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{4}(x) - 4cot^{4}(x)cot^{2}(csc(x))csc^{2}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) - 6cot^{3}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{3}(x)csc^{3}(csc(csc(x)))csc^{3}(csc(x)) + 2cot^{4}(x)cot(csc(csc(x)))csc^{2}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 3cot(csc(csc(x)))cot^{4}(x)cot(csc(x))csc^{3}(x)csc^{3}(csc(x))csc(csc(csc(x))) - 2cot^{3}(csc(x))cot^{4}(x)cot^{3}(csc(csc(x)))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 3cot^{2}(csc(x))cot(csc(csc(x)))cot^{4}(x)csc^{4}(x)csc^{3}(csc(csc(x)))csc^{5}(csc(x)) + 3cot^{4}(csc(x))cot^{3}(csc(csc(x)))cot^{4}(x)csc^{3}(csc(x))csc^{4}(x)csc(csc(csc(x))) - 3cot^{3}(csc(csc(x)))cot^{4}(x)cot^{3}(csc(x))csc^{3}(csc(x))csc^{3}(x)csc(csc(csc(x))) - cot^{4}(csc(csc(x)))cot^{4}(csc(x))cot^{4}(x)csc^{4}(csc(x))csc(csc(csc(x)))csc^{4}(x) - 4cot^{2}(csc(x))cot^{2}(x)csc^{4}(x)csc^{2}(csc(x))csc^{3}(csc(csc(x))) + 6cot^{2}(csc(csc(x)))cot^{3}(csc(x))cot^{4}(x)csc^{2}(csc(x))csc^{3}(x)csc(csc(csc(x))) + 2cot^{3}(csc(csc(x)))cot^{4}(csc(x))cot^{4}(x)csc^{3}(csc(x))csc(csc(csc(x)))csc^{4}(x)\\ \end{split}\end{equation} \]