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 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(x)cos(x)tan(x)cot(x)csc(x)sec(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(x)cos(x)tan(x)cot(x)sec(x)csc(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)cos(x)tan(x)cot(x)sec(x)csc(x)\right)}{dx}\\=&cos(x)cos(x)tan(x)cot(x)sec(x)csc(x) + sin(x)*-sin(x)tan(x)cot(x)sec(x)csc(x) + sin(x)cos(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + sin(x)cos(x)tan(x)*-csc^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)cot(x)sec(x)tan(x)csc(x) + sin(x)cos(x)tan(x)cot(x)sec(x)*-csc(x)cot(x)\\=&cos^{2}(x)tan(x)cot(x)sec(x)csc(x) - sin^{2}(x)tan(x)cot(x)sec(x)csc(x) + sin(x)cos(x)cot(x)sec^{3}(x)csc(x) - sin(x)cos(x)tan(x)sec(x)csc^{3}(x) + sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( cos^{2}(x)tan(x)cot(x)sec(x)csc(x) - sin^{2}(x)tan(x)cot(x)sec(x)csc(x) + sin(x)cos(x)cot(x)sec^{3}(x)csc(x) - sin(x)cos(x)tan(x)sec(x)csc^{3}(x) + sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x)\right)}{dx}\\=&-2cos(x)sin(x)tan(x)cot(x)sec(x)csc(x) + cos^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + cos^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc(x) + cos^{2}(x)tan(x)cot(x)sec(x)tan(x)csc(x) + cos^{2}(x)tan(x)cot(x)sec(x)*-csc(x)cot(x) - 2sin(x)cos(x)tan(x)cot(x)sec(x)csc(x) - sin^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - sin^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc(x) - sin^{2}(x)tan(x)cot(x)sec(x)tan(x)csc(x) - sin^{2}(x)tan(x)cot(x)sec(x)*-csc(x)cot(x) + cos(x)cos(x)cot(x)sec^{3}(x)csc(x) + sin(x)*-sin(x)cot(x)sec^{3}(x)csc(x) + sin(x)cos(x)*-csc^{2}(x)sec^{3}(x)csc(x) + sin(x)cos(x)cot(x)*3sec^{3}(x)tan(x)csc(x) + sin(x)cos(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - cos(x)cos(x)tan(x)sec(x)csc^{3}(x) - sin(x)*-sin(x)tan(x)sec(x)csc^{3}(x) - sin(x)cos(x)sec^{2}(x)(1)sec(x)csc^{3}(x) - sin(x)cos(x)tan(x)sec(x)tan(x)csc^{3}(x) - sin(x)cos(x)tan(x)sec(x)*-3csc^{3}(x)cot(x) + cos(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) + sin(x)*-sin(x)tan^{2}(x)cot(x)sec(x)csc(x) + sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + sin(x)cos(x)tan^{2}(x)*-csc^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan^{2}(x)cot(x)sec(x)tan(x)csc(x) + sin(x)cos(x)tan^{2}(x)cot(x)sec(x)*-csc(x)cot(x) - cos(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x) - sin(x)*-sin(x)tan(x)cot^{2}(x)sec(x)csc(x) - sin(x)cos(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{2}(x)sec(x)tan(x)csc(x) - sin(x)cos(x)tan(x)cot^{2}(x)sec(x)*-csc(x)cot(x)\\=&5sin(x)cos(x)tan(x)cot(x)sec(x)csc^{3}(x) + 2cos^{2}(x)cot(x)sec^{3}(x)csc(x) - 2cos^{2}(x)tan(x)sec(x)csc^{3}(x) + 2cos^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) - 2cos^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) - 4sin(x)cos(x)tan(x)cot(x)sec(x)csc(x) - 2sin^{2}(x)cot(x)sec^{3}(x)csc(x) + 2sin^{2}(x)tan(x)sec(x)csc^{3}(x) - 2sin^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) + 2sin^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) - 2sin(x)cos(x)sec^{3}(x)csc^{3}(x) + 5sin(x)cos(x)tan(x)cot(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)cot^{2}(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)sec(x)csc^{3}(x) + sin(x)cos(x)tan^{3}(x)cot(x)sec(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)cot^{3}(x)sec(x)csc(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 5sin(x)cos(x)tan(x)cot(x)sec(x)csc^{3}(x) + 2cos^{2}(x)cot(x)sec^{3}(x)csc(x) - 2cos^{2}(x)tan(x)sec(x)csc^{3}(x) + 2cos^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) - 2cos^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) - 4sin(x)cos(x)tan(x)cot(x)sec(x)csc(x) - 2sin^{2}(x)cot(x)sec^{3}(x)csc(x) + 2sin^{2}(x)tan(x)sec(x)csc^{3}(x) - 2sin^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) + 2sin^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) - 2sin(x)cos(x)sec^{3}(x)csc^{3}(x) + 5sin(x)cos(x)tan(x)cot(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)cot^{2}(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)sec(x)csc^{3}(x) + sin(x)cos(x)tan^{3}(x)cot(x)sec(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)cot^{3}(x)sec(x)csc(x)\right)}{dx}\\=&5cos(x)cos(x)tan(x)cot(x)sec(x)csc^{3}(x) + 5sin(x)*-sin(x)tan(x)cot(x)sec(x)csc^{3}(x) + 5sin(x)cos(x)sec^{2}(x)(1)cot(x)sec(x)csc^{3}(x) + 5sin(x)cos(x)tan(x)*-csc^{2}(x)sec(x)csc^{3}(x) + 5sin(x)cos(x)tan(x)cot(x)sec(x)tan(x)csc^{3}(x) + 5sin(x)cos(x)tan(x)cot(x)sec(x)*-3csc^{3}(x)cot(x) + 2*-2cos(x)sin(x)cot(x)sec^{3}(x)csc(x) + 2cos^{2}(x)*-csc^{2}(x)sec^{3}(x)csc(x) + 2cos^{2}(x)cot(x)*3sec^{3}(x)tan(x)csc(x) + 2cos^{2}(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - 2*-2cos(x)sin(x)tan(x)sec(x)csc^{3}(x) - 2cos^{2}(x)sec^{2}(x)(1)sec(x)csc^{3}(x) - 2cos^{2}(x)tan(x)sec(x)tan(x)csc^{3}(x) - 2cos^{2}(x)tan(x)sec(x)*-3csc^{3}(x)cot(x) + 2*-2cos(x)sin(x)tan^{2}(x)cot(x)sec(x)csc(x) + 2cos^{2}(x)*2tan(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + 2cos^{2}(x)tan^{2}(x)*-csc^{2}(x)sec(x)csc(x) + 2cos^{2}(x)tan^{2}(x)cot(x)sec(x)tan(x)csc(x) + 2cos^{2}(x)tan^{2}(x)cot(x)sec(x)*-csc(x)cot(x) - 2*-2cos(x)sin(x)tan(x)cot^{2}(x)sec(x)csc(x) - 2cos^{2}(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) - 2cos^{2}(x)tan(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) - 2cos^{2}(x)tan(x)cot^{2}(x)sec(x)tan(x)csc(x) - 2cos^{2}(x)tan(x)cot^{2}(x)sec(x)*-csc(x)cot(x) - 4cos(x)cos(x)tan(x)cot(x)sec(x)csc(x) - 4sin(x)*-sin(x)tan(x)cot(x)sec(x)csc(x) - 4sin(x)cos(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - 4sin(x)cos(x)tan(x)*-csc^{2}(x)sec(x)csc(x) - 4sin(x)cos(x)tan(x)cot(x)sec(x)tan(x)csc(x) - 4sin(x)cos(x)tan(x)cot(x)sec(x)*-csc(x)cot(x) - 2*2sin(x)cos(x)cot(x)sec^{3}(x)csc(x) - 2sin^{2}(x)*-csc^{2}(x)sec^{3}(x)csc(x) - 2sin^{2}(x)cot(x)*3sec^{3}(x)tan(x)csc(x) - 2sin^{2}(x)cot(x)sec^{3}(x)*-csc(x)cot(x) + 2*2sin(x)cos(x)tan(x)sec(x)csc^{3}(x) + 2sin^{2}(x)sec^{2}(x)(1)sec(x)csc^{3}(x) + 2sin^{2}(x)tan(x)sec(x)tan(x)csc^{3}(x) + 2sin^{2}(x)tan(x)sec(x)*-3csc^{3}(x)cot(x) - 2*2sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) - 2sin^{2}(x)*2tan(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - 2sin^{2}(x)tan^{2}(x)*-csc^{2}(x)sec(x)csc(x) - 2sin^{2}(x)tan^{2}(x)cot(x)sec(x)tan(x)csc(x) - 2sin^{2}(x)tan^{2}(x)cot(x)sec(x)*-csc(x)cot(x) + 2*2sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x) + 2sin^{2}(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) + 2sin^{2}(x)tan(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) + 2sin^{2}(x)tan(x)cot^{2}(x)sec(x)tan(x)csc(x) + 2sin^{2}(x)tan(x)cot^{2}(x)sec(x)*-csc(x)cot(x) - 2cos(x)cos(x)sec^{3}(x)csc^{3}(x) - 2sin(x)*-sin(x)sec^{3}(x)csc^{3}(x) - 2sin(x)cos(x)*3sec^{3}(x)tan(x)csc^{3}(x) - 2sin(x)cos(x)sec^{3}(x)*-3csc^{3}(x)cot(x) + 5cos(x)cos(x)tan(x)cot(x)sec^{3}(x)csc(x) + 5sin(x)*-sin(x)tan(x)cot(x)sec^{3}(x)csc(x) + 5sin(x)cos(x)sec^{2}(x)(1)cot(x)sec^{3}(x)csc(x) + 5sin(x)cos(x)tan(x)*-csc^{2}(x)sec^{3}(x)csc(x) + 5sin(x)cos(x)tan(x)cot(x)*3sec^{3}(x)tan(x)csc(x) + 5sin(x)cos(x)tan(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - 2cos(x)cos(x)cot^{2}(x)sec^{3}(x)csc(x) - 2sin(x)*-sin(x)cot^{2}(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)*-2cot(x)csc^{2}(x)sec^{3}(x)csc(x) - 2sin(x)cos(x)cot^{2}(x)*3sec^{3}(x)tan(x)csc(x) - 2sin(x)cos(x)cot^{2}(x)sec^{3}(x)*-csc(x)cot(x) - 2cos(x)cos(x)tan^{2}(x)sec(x)csc^{3}(x) - 2sin(x)*-sin(x)tan^{2}(x)sec(x)csc^{3}(x) - 2sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec(x)csc^{3}(x) - 2sin(x)cos(x)tan^{2}(x)sec(x)tan(x)csc^{3}(x) - 2sin(x)cos(x)tan^{2}(x)sec(x)*-3csc^{3}(x)cot(x) + cos(x)cos(x)tan^{3}(x)cot(x)sec(x)csc(x) + sin(x)*-sin(x)tan^{3}(x)cot(x)sec(x)csc(x) + sin(x)cos(x)*3tan^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + sin(x)cos(x)tan^{3}(x)*-csc^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan^{3}(x)cot(x)sec(x)tan(x)csc(x) + sin(x)cos(x)tan^{3}(x)cot(x)sec(x)*-csc(x)cot(x) - 2cos(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) - 2sin(x)*-sin(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) - 2sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)tan(x)csc(x) - 2sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)*-csc(x)cot(x) + cos(x)cos(x)tan(x)cot^{3}(x)sec(x)csc(x) + sin(x)*-sin(x)tan(x)cot^{3}(x)sec(x)csc(x) + sin(x)cos(x)sec^{2}(x)(1)cot^{3}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)*-3cot^{2}(x)csc^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)cot^{3}(x)sec(x)tan(x)csc(x) + sin(x)cos(x)tan(x)cot^{3}(x)sec(x)*-csc(x)cot(x)\\=&15cos^{2}(x)tan(x)cot(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec(x)csc^{3}(x) + 15sin(x)cos(x)cot(x)sec^{3}(x)csc^{3}(x) - 5sin(x)cos(x)tan(x)sec(x)csc^{5}(x) + 15sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) - 18sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 6cos^{2}(x)sec^{3}(x)csc^{3}(x) - 6cos^{2}(x)cot^{2}(x)sec^{3}(x)csc(x) + 12sin(x)cos(x)tan(x)sec(x)csc^{3}(x) - 6cos^{2}(x)tan^{2}(x)sec(x)csc^{3}(x) + 15cos^{2}(x)tan(x)cot(x)sec^{3}(x)csc(x) + 3cos^{2}(x)tan^{3}(x)cot(x)sec(x)csc(x) - 6cos^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + 3cos^{2}(x)tan(x)cot^{3}(x)sec(x)csc(x) - 4cos^{2}(x)tan(x)cot(x)sec(x)csc(x) + 4sin^{2}(x)tan(x)cot(x)sec(x)csc(x) - 12sin(x)cos(x)cot(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)sec^{3}(x)csc^{3}(x) - 12sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) + 12sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x) + 6sin^{2}(x)sec^{3}(x)csc^{3}(x) + 6sin^{2}(x)cot^{2}(x)sec^{3}(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)sec(x)csc^{3}(x) + 6sin^{2}(x)tan^{2}(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec^{3}(x)csc(x) - 3sin^{2}(x)tan^{3}(x)cot(x)sec(x)csc(x) + 6sin^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) - 3sin^{2}(x)tan(x)cot^{3}(x)sec(x)csc(x) + 5sin(x)cos(x)cot(x)sec^{5}(x)csc(x) + 18sin(x)cos(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) + 3sin(x)cos(x)cot^{3}(x)sec^{3}(x)csc(x) + sin(x)cos(x)tan^{4}(x)cot(x)sec(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) + 3sin(x)cos(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{4}(x)sec(x)csc(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 15cos^{2}(x)tan(x)cot(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec(x)csc^{3}(x) + 15sin(x)cos(x)cot(x)sec^{3}(x)csc^{3}(x) - 5sin(x)cos(x)tan(x)sec(x)csc^{5}(x) + 15sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) - 18sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 6cos^{2}(x)sec^{3}(x)csc^{3}(x) - 6cos^{2}(x)cot^{2}(x)sec^{3}(x)csc(x) + 12sin(x)cos(x)tan(x)sec(x)csc^{3}(x) - 6cos^{2}(x)tan^{2}(x)sec(x)csc^{3}(x) + 15cos^{2}(x)tan(x)cot(x)sec^{3}(x)csc(x) + 3cos^{2}(x)tan^{3}(x)cot(x)sec(x)csc(x) - 6cos^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + 3cos^{2}(x)tan(x)cot^{3}(x)sec(x)csc(x) - 4cos^{2}(x)tan(x)cot(x)sec(x)csc(x) + 4sin^{2}(x)tan(x)cot(x)sec(x)csc(x) - 12sin(x)cos(x)cot(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)sec^{3}(x)csc^{3}(x) - 12sin(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) + 12sin(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x) + 6sin^{2}(x)sec^{3}(x)csc^{3}(x) + 6sin^{2}(x)cot^{2}(x)sec^{3}(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)sec(x)csc^{3}(x) + 6sin^{2}(x)tan^{2}(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec^{3}(x)csc(x) - 3sin^{2}(x)tan^{3}(x)cot(x)sec(x)csc(x) + 6sin^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) - 3sin^{2}(x)tan(x)cot^{3}(x)sec(x)csc(x) + 5sin(x)cos(x)cot(x)sec^{5}(x)csc(x) + 18sin(x)cos(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) + 3sin(x)cos(x)cot^{3}(x)sec^{3}(x)csc(x) + sin(x)cos(x)tan^{4}(x)cot(x)sec(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) + 3sin(x)cos(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{4}(x)sec(x)csc(x)\right)}{dx}\\=&15*-2cos(x)sin(x)tan(x)cot(x)sec(x)csc^{3}(x) + 15cos^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc^{3}(x) + 15cos^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc^{3}(x) + 15cos^{2}(x)tan(x)cot(x)sec(x)tan(x)csc^{3}(x) + 15cos^{2}(x)tan(x)cot(x)sec(x)*-3csc^{3}(x)cot(x) - 15*2sin(x)cos(x)tan(x)cot(x)sec(x)csc^{3}(x) - 15sin^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec(x)tan(x)csc^{3}(x) - 15sin^{2}(x)tan(x)cot(x)sec(x)*-3csc^{3}(x)cot(x) + 15cos(x)cos(x)cot(x)sec^{3}(x)csc^{3}(x) + 15sin(x)*-sin(x)cot(x)sec^{3}(x)csc^{3}(x) + 15sin(x)cos(x)*-csc^{2}(x)sec^{3}(x)csc^{3}(x) + 15sin(x)cos(x)cot(x)*3sec^{3}(x)tan(x)csc^{3}(x) + 15sin(x)cos(x)cot(x)sec^{3}(x)*-3csc^{3}(x)cot(x) - 5cos(x)cos(x)tan(x)sec(x)csc^{5}(x) - 5sin(x)*-sin(x)tan(x)sec(x)csc^{5}(x) - 5sin(x)cos(x)sec^{2}(x)(1)sec(x)csc^{5}(x) - 5sin(x)cos(x)tan(x)sec(x)tan(x)csc^{5}(x) - 5sin(x)cos(x)tan(x)sec(x)*-5csc^{5}(x)cot(x) + 15cos(x)cos(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) + 15sin(x)*-sin(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) + 15sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot(x)sec(x)csc^{3}(x) + 15sin(x)cos(x)tan^{2}(x)*-csc^{2}(x)sec(x)csc^{3}(x) + 15sin(x)cos(x)tan^{2}(x)cot(x)sec(x)tan(x)csc^{3}(x) + 15sin(x)cos(x)tan^{2}(x)cot(x)sec(x)*-3csc^{3}(x)cot(x) - 18cos(x)cos(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 18sin(x)*-sin(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 18sin(x)cos(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc^{3}(x) - 18sin(x)cos(x)tan(x)*-2cot(x)csc^{2}(x)sec(x)csc^{3}(x) - 18sin(x)cos(x)tan(x)cot^{2}(x)sec(x)tan(x)csc^{3}(x) - 18sin(x)cos(x)tan(x)cot^{2}(x)sec(x)*-3csc^{3}(x)cot(x) - 6*-2cos(x)sin(x)sec^{3}(x)csc^{3}(x) - 6cos^{2}(x)*3sec^{3}(x)tan(x)csc^{3}(x) - 6cos^{2}(x)sec^{3}(x)*-3csc^{3}(x)cot(x) - 6*-2cos(x)sin(x)cot^{2}(x)sec^{3}(x)csc(x) - 6cos^{2}(x)*-2cot(x)csc^{2}(x)sec^{3}(x)csc(x) - 6cos^{2}(x)cot^{2}(x)*3sec^{3}(x)tan(x)csc(x) - 6cos^{2}(x)cot^{2}(x)sec^{3}(x)*-csc(x)cot(x) + 12cos(x)cos(x)tan(x)sec(x)csc^{3}(x) + 12sin(x)*-sin(x)tan(x)sec(x)csc^{3}(x) + 12sin(x)cos(x)sec^{2}(x)(1)sec(x)csc^{3}(x) + 12sin(x)cos(x)tan(x)sec(x)tan(x)csc^{3}(x) + 12sin(x)cos(x)tan(x)sec(x)*-3csc^{3}(x)cot(x) - 6*-2cos(x)sin(x)tan^{2}(x)sec(x)csc^{3}(x) - 6cos^{2}(x)*2tan(x)sec^{2}(x)(1)sec(x)csc^{3}(x) - 6cos^{2}(x)tan^{2}(x)sec(x)tan(x)csc^{3}(x) - 6cos^{2}(x)tan^{2}(x)sec(x)*-3csc^{3}(x)cot(x) + 15*-2cos(x)sin(x)tan(x)cot(x)sec^{3}(x)csc(x) + 15cos^{2}(x)sec^{2}(x)(1)cot(x)sec^{3}(x)csc(x) + 15cos^{2}(x)tan(x)*-csc^{2}(x)sec^{3}(x)csc(x) + 15cos^{2}(x)tan(x)cot(x)*3sec^{3}(x)tan(x)csc(x) + 15cos^{2}(x)tan(x)cot(x)sec^{3}(x)*-csc(x)cot(x) + 3*-2cos(x)sin(x)tan^{3}(x)cot(x)sec(x)csc(x) + 3cos^{2}(x)*3tan^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + 3cos^{2}(x)tan^{3}(x)*-csc^{2}(x)sec(x)csc(x) + 3cos^{2}(x)tan^{3}(x)cot(x)sec(x)tan(x)csc(x) + 3cos^{2}(x)tan^{3}(x)cot(x)sec(x)*-csc(x)cot(x) - 6*-2cos(x)sin(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) - 6cos^{2}(x)*2tan(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) - 6cos^{2}(x)tan^{2}(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) - 6cos^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)tan(x)csc(x) - 6cos^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)*-csc(x)cot(x) + 3*-2cos(x)sin(x)tan(x)cot^{3}(x)sec(x)csc(x) + 3cos^{2}(x)sec^{2}(x)(1)cot^{3}(x)sec(x)csc(x) + 3cos^{2}(x)tan(x)*-3cot^{2}(x)csc^{2}(x)sec(x)csc(x) + 3cos^{2}(x)tan(x)cot^{3}(x)sec(x)tan(x)csc(x) + 3cos^{2}(x)tan(x)cot^{3}(x)sec(x)*-csc(x)cot(x) - 4*-2cos(x)sin(x)tan(x)cot(x)sec(x)csc(x) - 4cos^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - 4cos^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc(x) - 4cos^{2}(x)tan(x)cot(x)sec(x)tan(x)csc(x) - 4cos^{2}(x)tan(x)cot(x)sec(x)*-csc(x)cot(x) + 4*2sin(x)cos(x)tan(x)cot(x)sec(x)csc(x) + 4sin^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + 4sin^{2}(x)tan(x)*-csc^{2}(x)sec(x)csc(x) + 4sin^{2}(x)tan(x)cot(x)sec(x)tan(x)csc(x) + 4sin^{2}(x)tan(x)cot(x)sec(x)*-csc(x)cot(x) - 12cos(x)cos(x)cot(x)sec^{3}(x)csc(x) - 12sin(x)*-sin(x)cot(x)sec^{3}(x)csc(x) - 12sin(x)cos(x)*-csc^{2}(x)sec^{3}(x)csc(x) - 12sin(x)cos(x)cot(x)*3sec^{3}(x)tan(x)csc(x) - 12sin(x)cos(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - 15cos(x)cos(x)tan(x)sec^{3}(x)csc^{3}(x) - 15sin(x)*-sin(x)tan(x)sec^{3}(x)csc^{3}(x) - 15sin(x)cos(x)sec^{2}(x)(1)sec^{3}(x)csc^{3}(x) - 15sin(x)cos(x)tan(x)*3sec^{3}(x)tan(x)csc^{3}(x) - 15sin(x)cos(x)tan(x)sec^{3}(x)*-3csc^{3}(x)cot(x) - 12cos(x)cos(x)tan^{2}(x)cot(x)sec(x)csc(x) - 12sin(x)*-sin(x)tan^{2}(x)cot(x)sec(x)csc(x) - 12sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - 12sin(x)cos(x)tan^{2}(x)*-csc^{2}(x)sec(x)csc(x) - 12sin(x)cos(x)tan^{2}(x)cot(x)sec(x)tan(x)csc(x) - 12sin(x)cos(x)tan^{2}(x)cot(x)sec(x)*-csc(x)cot(x) + 12cos(x)cos(x)tan(x)cot^{2}(x)sec(x)csc(x) + 12sin(x)*-sin(x)tan(x)cot^{2}(x)sec(x)csc(x) + 12sin(x)cos(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) + 12sin(x)cos(x)tan(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) + 12sin(x)cos(x)tan(x)cot^{2}(x)sec(x)tan(x)csc(x) + 12sin(x)cos(x)tan(x)cot^{2}(x)sec(x)*-csc(x)cot(x) + 6*2sin(x)cos(x)sec^{3}(x)csc^{3}(x) + 6sin^{2}(x)*3sec^{3}(x)tan(x)csc^{3}(x) + 6sin^{2}(x)sec^{3}(x)*-3csc^{3}(x)cot(x) + 6*2sin(x)cos(x)cot^{2}(x)sec^{3}(x)csc(x) + 6sin^{2}(x)*-2cot(x)csc^{2}(x)sec^{3}(x)csc(x) + 6sin^{2}(x)cot^{2}(x)*3sec^{3}(x)tan(x)csc(x) + 6sin^{2}(x)cot^{2}(x)sec^{3}(x)*-csc(x)cot(x) - 3cos(x)cos(x)tan^{3}(x)sec(x)csc^{3}(x) - 3sin(x)*-sin(x)tan^{3}(x)sec(x)csc^{3}(x) - 3sin(x)cos(x)*3tan^{2}(x)sec^{2}(x)(1)sec(x)csc^{3}(x) - 3sin(x)cos(x)tan^{3}(x)sec(x)tan(x)csc^{3}(x) - 3sin(x)cos(x)tan^{3}(x)sec(x)*-3csc^{3}(x)cot(x) + 6*2sin(x)cos(x)tan^{2}(x)sec(x)csc^{3}(x) + 6sin^{2}(x)*2tan(x)sec^{2}(x)(1)sec(x)csc^{3}(x) + 6sin^{2}(x)tan^{2}(x)sec(x)tan(x)csc^{3}(x) + 6sin^{2}(x)tan^{2}(x)sec(x)*-3csc^{3}(x)cot(x) - 15*2sin(x)cos(x)tan(x)cot(x)sec^{3}(x)csc(x) - 15sin^{2}(x)sec^{2}(x)(1)cot(x)sec^{3}(x)csc(x) - 15sin^{2}(x)tan(x)*-csc^{2}(x)sec^{3}(x)csc(x) - 15sin^{2}(x)tan(x)cot(x)*3sec^{3}(x)tan(x)csc(x) - 15sin^{2}(x)tan(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - 3*2sin(x)cos(x)tan^{3}(x)cot(x)sec(x)csc(x) - 3sin^{2}(x)*3tan^{2}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) - 3sin^{2}(x)tan^{3}(x)*-csc^{2}(x)sec(x)csc(x) - 3sin^{2}(x)tan^{3}(x)cot(x)sec(x)tan(x)csc(x) - 3sin^{2}(x)tan^{3}(x)cot(x)sec(x)*-csc(x)cot(x) + 6*2sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + 6sin^{2}(x)*2tan(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) + 6sin^{2}(x)tan^{2}(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) + 6sin^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)tan(x)csc(x) + 6sin^{2}(x)tan^{2}(x)cot^{2}(x)sec(x)*-csc(x)cot(x) - 3*2sin(x)cos(x)tan(x)cot^{3}(x)sec(x)csc(x) - 3sin^{2}(x)sec^{2}(x)(1)cot^{3}(x)sec(x)csc(x) - 3sin^{2}(x)tan(x)*-3cot^{2}(x)csc^{2}(x)sec(x)csc(x) - 3sin^{2}(x)tan(x)cot^{3}(x)sec(x)tan(x)csc(x) - 3sin^{2}(x)tan(x)cot^{3}(x)sec(x)*-csc(x)cot(x) + 5cos(x)cos(x)cot(x)sec^{5}(x)csc(x) + 5sin(x)*-sin(x)cot(x)sec^{5}(x)csc(x) + 5sin(x)cos(x)*-csc^{2}(x)sec^{5}(x)csc(x) + 5sin(x)cos(x)cot(x)*5sec^{5}(x)tan(x)csc(x) + 5sin(x)cos(x)cot(x)sec^{5}(x)*-csc(x)cot(x) + 18cos(x)cos(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) + 18sin(x)*-sin(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) + 18sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot(x)sec^{3}(x)csc(x) + 18sin(x)cos(x)tan^{2}(x)*-csc^{2}(x)sec^{3}(x)csc(x) + 18sin(x)cos(x)tan^{2}(x)cot(x)*3sec^{3}(x)tan(x)csc(x) + 18sin(x)cos(x)tan^{2}(x)cot(x)sec^{3}(x)*-csc(x)cot(x) - 15cos(x)cos(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) - 15sin(x)*-sin(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)sec^{2}(x)(1)cot^{2}(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)*-2cot(x)csc^{2}(x)sec^{3}(x)csc(x) - 15sin(x)cos(x)tan(x)cot^{2}(x)*3sec^{3}(x)tan(x)csc(x) - 15sin(x)cos(x)tan(x)cot^{2}(x)sec^{3}(x)*-csc(x)cot(x) + 3cos(x)cos(x)cot^{3}(x)sec^{3}(x)csc(x) + 3sin(x)*-sin(x)cot^{3}(x)sec^{3}(x)csc(x) + 3sin(x)cos(x)*-3cot^{2}(x)csc^{2}(x)sec^{3}(x)csc(x) + 3sin(x)cos(x)cot^{3}(x)*3sec^{3}(x)tan(x)csc(x) + 3sin(x)cos(x)cot^{3}(x)sec^{3}(x)*-csc(x)cot(x) + cos(x)cos(x)tan^{4}(x)cot(x)sec(x)csc(x) + sin(x)*-sin(x)tan^{4}(x)cot(x)sec(x)csc(x) + sin(x)cos(x)*4tan^{3}(x)sec^{2}(x)(1)cot(x)sec(x)csc(x) + sin(x)cos(x)tan^{4}(x)*-csc^{2}(x)sec(x)csc(x) + sin(x)cos(x)tan^{4}(x)cot(x)sec(x)tan(x)csc(x) + sin(x)cos(x)tan^{4}(x)cot(x)sec(x)*-csc(x)cot(x) - 3cos(x)cos(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) - 3sin(x)*-sin(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) - 3sin(x)cos(x)*3tan^{2}(x)sec^{2}(x)(1)cot^{2}(x)sec(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)*-2cot(x)csc^{2}(x)sec(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)cot^{2}(x)sec(x)tan(x)csc(x) - 3sin(x)cos(x)tan^{3}(x)cot^{2}(x)sec(x)*-csc(x)cot(x) + 3cos(x)cos(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) + 3sin(x)*-sin(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) + 3sin(x)cos(x)*2tan(x)sec^{2}(x)(1)cot^{3}(x)sec(x)csc(x) + 3sin(x)cos(x)tan^{2}(x)*-3cot^{2}(x)csc^{2}(x)sec(x)csc(x) + 3sin(x)cos(x)tan^{2}(x)cot^{3}(x)sec(x)tan(x)csc(x) + 3sin(x)cos(x)tan^{2}(x)cot^{3}(x)sec(x)*-csc(x)cot(x) - cos(x)cos(x)tan(x)cot^{4}(x)sec(x)csc(x) - sin(x)*-sin(x)tan(x)cot^{4}(x)sec(x)csc(x) - sin(x)cos(x)sec^{2}(x)(1)cot^{4}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)*-4cot^{3}(x)csc^{2}(x)sec(x)csc(x) - sin(x)cos(x)tan(x)cot^{4}(x)sec(x)tan(x)csc(x) - sin(x)cos(x)tan(x)cot^{4}(x)sec(x)*-csc(x)cot(x)\\=&61sin(x)cos(x)tan(x)cot(x)sec(x)csc^{5}(x) + 60cos^{2}(x)cot(x)sec^{3}(x)csc^{3}(x) - 20cos^{2}(x)tan(x)sec(x)csc^{5}(x) + 60cos^{2}(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) - 72cos^{2}(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 120sin(x)cos(x)tan(x)cot(x)sec(x)csc^{3}(x) - 60sin^{2}(x)cot(x)sec^{3}(x)csc^{3}(x) + 20sin^{2}(x)tan(x)sec(x)csc^{5}(x) - 60sin^{2}(x)tan^{2}(x)cot(x)sec(x)csc^{3}(x) + 72sin^{2}(x)tan(x)cot^{2}(x)sec(x)csc^{3}(x) - 20sin(x)cos(x)sec^{3}(x)csc^{5}(x) + 150sin(x)cos(x)tan(x)cot(x)sec^{3}(x)csc^{3}(x) - 72sin(x)cos(x)cot^{2}(x)sec^{3}(x)csc^{3}(x) - 20sin(x)cos(x)tan^{2}(x)sec(x)csc^{5}(x) + 30sin(x)cos(x)tan^{3}(x)cot(x)sec(x)csc^{3}(x) - 72sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc^{3}(x) + 58sin(x)cos(x)tan(x)cot^{3}(x)sec(x)csc^{3}(x) + 48sin(x)cos(x)sec^{3}(x)csc^{3}(x) - 60cos^{2}(x)tan(x)sec^{3}(x)csc^{3}(x) + 12cos^{2}(x)cot^{3}(x)sec^{3}(x)csc(x) + 16cos^{2}(x)tan(x)sec(x)csc^{3}(x) - 16sin^{2}(x)tan(x)sec(x)csc^{3}(x) + 48sin(x)cos(x)tan^{2}(x)sec(x)csc^{3}(x) - 12cos^{2}(x)tan^{3}(x)sec(x)csc^{3}(x) - 120sin(x)cos(x)tan(x)cot(x)sec^{3}(x)csc(x) + 20cos^{2}(x)cot(x)sec^{5}(x)csc(x) + 72cos^{2}(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) - 60cos^{2}(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) - 24sin(x)cos(x)tan^{3}(x)cot(x)sec(x)csc(x) + 4cos^{2}(x)tan^{4}(x)cot(x)sec(x)csc(x) - 12cos^{2}(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) + 48sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec(x)csc(x) + 12cos^{2}(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) - 24sin(x)cos(x)tan(x)cot^{3}(x)sec(x)csc(x) - 4cos^{2}(x)tan(x)cot^{4}(x)sec(x)csc(x) + 16sin(x)cos(x)tan(x)cot(x)sec(x)csc(x) - 16cos^{2}(x)cot(x)sec^{3}(x)csc(x) - 16cos^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) + 16cos^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) + 16sin^{2}(x)cot(x)sec^{3}(x)csc(x) + 16sin^{2}(x)tan^{2}(x)cot(x)sec(x)csc(x) - 16sin^{2}(x)tan(x)cot^{2}(x)sec(x)csc(x) - 20sin(x)cos(x)sec^{5}(x)csc^{3}(x) + 48sin(x)cos(x)cot^{2}(x)sec^{3}(x)csc(x) + 60sin^{2}(x)tan(x)sec^{3}(x)csc^{3}(x) - 72sin(x)cos(x)tan^{2}(x)sec^{3}(x)csc^{3}(x) - 12sin^{2}(x)cot^{3}(x)sec^{3}(x)csc(x) + 12sin^{2}(x)tan^{3}(x)sec(x)csc^{3}(x) - 4sin(x)cos(x)tan^{4}(x)sec(x)csc^{3}(x) - 20sin^{2}(x)cot(x)sec^{5}(x)csc(x) - 72sin^{2}(x)tan^{2}(x)cot(x)sec^{3}(x)csc(x) + 60sin^{2}(x)tan(x)cot^{2}(x)sec^{3}(x)csc(x) - 4sin^{2}(x)tan^{4}(x)cot(x)sec(x)csc(x) + 12sin^{2}(x)tan^{3}(x)cot^{2}(x)sec(x)csc(x) - 12sin^{2}(x)tan^{2}(x)cot^{3}(x)sec(x)csc(x) + 4sin^{2}(x)tan(x)cot^{4}(x)sec(x)csc(x) + 61sin(x)cos(x)tan(x)cot(x)sec^{5}(x)csc(x) - 20sin(x)cos(x)cot^{2}(x)sec^{5}(x)csc(x) + 58sin(x)cos(x)tan^{3}(x)cot(x)sec^{3}(x)csc(x) - 72sin(x)cos(x)tan^{2}(x)cot^{2}(x)sec^{3}(x)csc(x) + 30sin(x)cos(x)tan(x)cot^{3}(x)sec^{3}(x)csc(x) - 4sin(x)cos(x)cot^{4}(x)sec^{3}(x)csc(x) + sin(x)cos(x)tan^{5}(x)cot(x)sec(x)csc(x) - 4sin(x)cos(x)tan^{4}(x)cot^{2}(x)sec(x)csc(x) + 6sin(x)cos(x)tan^{3}(x)cot^{3}(x)sec(x)csc(x) - 4sin(x)cos(x)tan^{2}(x)cot^{4}(x)sec(x)csc(x) + sin(x)cos(x)tan(x)cot^{5}(x)sec(x)csc(x)\\ \end{split}\end{equation} \]