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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{cos(x)sin(x)ln(x)}{sin(cos(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ln(x)sin(x)cos(x)}{sin(cos(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{ln(x)sin(x)cos(x)}{sin(cos(x))}\right)}{dx}\\=&\frac{sin(x)cos(x)}{(x)sin(cos(x))} + \frac{ln(x)cos(x)cos(x)}{sin(cos(x))} + \frac{ln(x)sin(x)*-cos(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin(x)*-sin(x)}{sin(cos(x))}\\=&\frac{sin(x)cos(x)}{xsin(cos(x))} + \frac{ln(x)cos^{2}(x)}{sin(cos(x))} + \frac{ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{ln(x)sin^{2}(x)}{sin(cos(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(x)cos(x)}{xsin(cos(x))} + \frac{ln(x)cos^{2}(x)}{sin(cos(x))} + \frac{ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{ln(x)sin^{2}(x)}{sin(cos(x))}\right)}{dx}\\=&\frac{-sin(x)cos(x)}{x^{2}sin(cos(x))} + \frac{cos(x)cos(x)}{xsin(cos(x))} + \frac{sin(x)*-cos(cos(x))*-sin(x)cos(x)}{xsin^{2}(cos(x))} + \frac{sin(x)*-sin(x)}{xsin(cos(x))} + \frac{cos^{2}(x)}{(x)sin(cos(x))} + \frac{ln(x)*-cos(cos(x))*-sin(x)cos^{2}(x)}{sin^{2}(cos(x))} + \frac{ln(x)*-2cos(x)sin(x)}{sin(cos(x))} + \frac{sin^{2}(x)cos(cos(x))cos(x)}{(x)sin^{2}(cos(x))} + \frac{ln(x)*-2cos(cos(x))*-sin(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{3}(cos(x))} + \frac{ln(x)*2sin(x)cos(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin^{2}(x)cos(cos(x))*-sin(x)}{sin^{2}(cos(x))} - \frac{sin^{2}(x)}{(x)sin(cos(x))} - \frac{ln(x)*2sin(x)cos(x)}{sin(cos(x))} - \frac{ln(x)sin^{2}(x)*-cos(cos(x))*-sin(x)}{sin^{2}(cos(x))}\\=&\frac{2sin^{2}(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} + \frac{2cos^{2}(x)}{xsin(cos(x))} - \frac{sin(x)cos(x)}{x^{2}sin(cos(x))} - \frac{2sin^{2}(x)}{xsin(cos(x))} + \frac{ln(x)sin(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} + \frac{2ln(x)sin(x)cos^{2}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{2ln(x)sin^{3}(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{4ln(x)sin(x)cos(x)}{sin(cos(x))} + \frac{ln(x)sin^{3}(x)cos(x)}{sin(cos(x))} - \frac{2ln(x)sin^{3}(x)cos(cos(x))}{sin^{2}(cos(x))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2sin^{2}(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} + \frac{2cos^{2}(x)}{xsin(cos(x))} - \frac{sin(x)cos(x)}{x^{2}sin(cos(x))} - \frac{2sin^{2}(x)}{xsin(cos(x))} + \frac{ln(x)sin(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} + \frac{2ln(x)sin(x)cos^{2}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{2ln(x)sin^{3}(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{4ln(x)sin(x)cos(x)}{sin(cos(x))} + \frac{ln(x)sin^{3}(x)cos(x)}{sin(cos(x))} - \frac{2ln(x)sin^{3}(x)cos(cos(x))}{sin^{2}(cos(x))}\right)}{dx}\\=&\frac{2*-sin^{2}(x)cos(cos(x))cos(x)}{x^{2}sin^{2}(cos(x))} + \frac{2*-2cos(cos(x))*-sin(x)sin^{2}(x)cos(cos(x))cos(x)}{xsin^{3}(cos(x))} + \frac{2*2sin(x)cos(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} + \frac{2sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x)}{xsin^{2}(cos(x))} + \frac{2sin^{2}(x)cos(cos(x))*-sin(x)}{xsin^{2}(cos(x))} + \frac{2*-cos^{2}(x)}{x^{2}sin(cos(x))} + \frac{2*-cos(cos(x))*-sin(x)cos^{2}(x)}{xsin^{2}(cos(x))} + \frac{2*-2cos(x)sin(x)}{xsin(cos(x))} - \frac{-2sin(x)cos(x)}{x^{3}sin(cos(x))} - \frac{cos(x)cos(x)}{x^{2}sin(cos(x))} - \frac{sin(x)*-cos(cos(x))*-sin(x)cos(x)}{x^{2}sin^{2}(cos(x))} - \frac{sin(x)*-sin(x)}{x^{2}sin(cos(x))} - \frac{2*-sin^{2}(x)}{x^{2}sin(cos(x))} - \frac{2*2sin(x)cos(x)}{xsin(cos(x))} - \frac{2sin^{2}(x)*-cos(cos(x))*-sin(x)}{xsin^{2}(cos(x))} + \frac{sin(x)cos(cos(x))cos^{2}(x)}{(x)sin^{2}(cos(x))} + \frac{ln(x)cos(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin(x)*-2cos(cos(x))*-sin(x)cos(cos(x))cos^{2}(x)}{sin^{3}(cos(x))} + \frac{ln(x)sin(x)*-sin(cos(x))*-sin(x)cos^{2}(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin(x)cos(cos(x))*-2cos(x)sin(x)}{sin^{2}(cos(x))} + \frac{2sin(x)cos^{2}(x)cos(cos(x))}{(x)sin^{2}(cos(x))} + \frac{2ln(x)cos(x)cos^{2}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{2ln(x)sin(x)*-2cos(cos(x))*-sin(x)cos^{2}(x)cos(cos(x))}{sin^{3}(cos(x))} + \frac{2ln(x)sin(x)*-2cos(x)sin(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{2ln(x)sin(x)cos^{2}(x)*-sin(cos(x))*-sin(x)}{sin^{2}(cos(x))} + \frac{2sin^{3}(x)cos^{2}(cos(x))cos(x)}{(x)sin^{3}(cos(x))} + \frac{2ln(x)*3sin^{2}(x)cos(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} + \frac{2ln(x)sin^{3}(x)*-3cos(cos(x))*-sin(x)cos^{2}(cos(x))cos(x)}{sin^{4}(cos(x))} + \frac{2ln(x)sin^{3}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)}{sin^{3}(cos(x))} + \frac{2ln(x)sin^{3}(x)cos^{2}(cos(x))*-sin(x)}{sin^{3}(cos(x))} - \frac{4sin(x)cos(x)}{(x)sin(cos(x))} - \frac{4ln(x)cos(x)cos(x)}{sin(cos(x))} - \frac{4ln(x)sin(x)*-cos(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} - \frac{4ln(x)sin(x)*-sin(x)}{sin(cos(x))} + \frac{sin^{3}(x)cos(x)}{(x)sin(cos(x))} + \frac{ln(x)*3sin^{2}(x)cos(x)cos(x)}{sin(cos(x))} + \frac{ln(x)sin^{3}(x)*-cos(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} + \frac{ln(x)sin^{3}(x)*-sin(x)}{sin(cos(x))} - \frac{2sin^{3}(x)cos(cos(x))}{(x)sin^{2}(cos(x))} - \frac{2ln(x)*-2cos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))}{sin^{3}(cos(x))} - \frac{2ln(x)*3sin^{2}(x)cos(x)cos(cos(x))}{sin^{2}(cos(x))} - \frac{2ln(x)sin^{3}(x)*-sin(cos(x))*-sin(x)}{sin^{2}(cos(x))}\\=&\frac{-3sin^{2}(x)cos(cos(x))cos(x)}{x^{2}sin^{2}(cos(x))} + \frac{6sin^{3}(x)cos^{2}(cos(x))cos(x)}{xsin^{3}(cos(x))} + \frac{6sin(x)cos^{2}(x)cos(cos(x))}{xsin^{2}(cos(x))} + \frac{3sin(x)cos(cos(x))cos^{2}(x)}{xsin^{2}(cos(x))} - \frac{6sin^{3}(x)cos(cos(x))}{xsin^{2}(cos(x))} - \frac{3cos^{2}(x)}{x^{2}sin(cos(x))} + \frac{3sin^{3}(x)cos(x)}{xsin(cos(x))} + \frac{2sin(x)cos(x)}{x^{3}sin(cos(x))} - \frac{12sin(x)cos(x)}{xsin(cos(x))} + \frac{3ln(x)cos^{3}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(cos(x))cos^{2}(x)}{sin^{3}(cos(x))} + \frac{5ln(x)sin^{4}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{2ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} + \frac{3sin^{2}(x)}{x^{2}sin(cos(x))} - \frac{10ln(x)sin^{2}(x)cos(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{4}(x)cos^{3}(cos(x))cos(x)}{sin^{4}(cos(x))} - \frac{4ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{6ln(x)sin^{4}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} - \frac{4ln(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)cos^{2}(x)}{sin(cos(x))} + \frac{4ln(x)sin^{2}(x)}{sin(cos(x))} - \frac{3ln(x)sin^{4}(x)}{sin(cos(x))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3sin^{2}(x)cos(cos(x))cos(x)}{x^{2}sin^{2}(cos(x))} + \frac{6sin^{3}(x)cos^{2}(cos(x))cos(x)}{xsin^{3}(cos(x))} + \frac{6sin(x)cos^{2}(x)cos(cos(x))}{xsin^{2}(cos(x))} + \frac{3sin(x)cos(cos(x))cos^{2}(x)}{xsin^{2}(cos(x))} - \frac{6sin^{3}(x)cos(cos(x))}{xsin^{2}(cos(x))} - \frac{3cos^{2}(x)}{x^{2}sin(cos(x))} + \frac{3sin^{3}(x)cos(x)}{xsin(cos(x))} + \frac{2sin(x)cos(x)}{x^{3}sin(cos(x))} - \frac{12sin(x)cos(x)}{xsin(cos(x))} + \frac{3ln(x)cos^{3}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(cos(x))cos^{2}(x)}{sin^{3}(cos(x))} + \frac{5ln(x)sin^{4}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{2ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} + \frac{3sin^{2}(x)}{x^{2}sin(cos(x))} - \frac{10ln(x)sin^{2}(x)cos(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{4}(x)cos^{3}(cos(x))cos(x)}{sin^{4}(cos(x))} - \frac{4ln(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{6ln(x)sin^{4}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} - \frac{4ln(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)cos^{2}(x)}{sin(cos(x))} + \frac{4ln(x)sin^{2}(x)}{sin(cos(x))} - \frac{3ln(x)sin^{4}(x)}{sin(cos(x))}\right)}{dx}\\=&\frac{-3*-2sin^{2}(x)cos(cos(x))cos(x)}{x^{3}sin^{2}(cos(x))} - \frac{3*-2cos(cos(x))*-sin(x)sin^{2}(x)cos(cos(x))cos(x)}{x^{2}sin^{3}(cos(x))} - \frac{3*2sin(x)cos(x)cos(cos(x))cos(x)}{x^{2}sin^{2}(cos(x))} - \frac{3sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x)}{x^{2}sin^{2}(cos(x))} - \frac{3sin^{2}(x)cos(cos(x))*-sin(x)}{x^{2}sin^{2}(cos(x))} + \frac{6*-sin^{3}(x)cos^{2}(cos(x))cos(x)}{x^{2}sin^{3}(cos(x))} + \frac{6*3sin^{2}(x)cos(x)cos^{2}(cos(x))cos(x)}{xsin^{3}(cos(x))} + \frac{6sin^{3}(x)*-3cos(cos(x))*-sin(x)cos^{2}(cos(x))cos(x)}{xsin^{4}(cos(x))} + \frac{6sin^{3}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)}{xsin^{3}(cos(x))} + \frac{6sin^{3}(x)cos^{2}(cos(x))*-sin(x)}{xsin^{3}(cos(x))} + \frac{6*-sin(x)cos^{2}(x)cos(cos(x))}{x^{2}sin^{2}(cos(x))} + \frac{6cos(x)cos^{2}(x)cos(cos(x))}{xsin^{2}(cos(x))} + \frac{6sin(x)*-2cos(cos(x))*-sin(x)cos^{2}(x)cos(cos(x))}{xsin^{3}(cos(x))} + \frac{6sin(x)*-2cos(x)sin(x)cos(cos(x))}{xsin^{2}(cos(x))} + \frac{6sin(x)cos^{2}(x)*-sin(cos(x))*-sin(x)}{xsin^{2}(cos(x))} + \frac{3*-sin(x)cos(cos(x))cos^{2}(x)}{x^{2}sin^{2}(cos(x))} + \frac{3cos(x)cos(cos(x))cos^{2}(x)}{xsin^{2}(cos(x))} + \frac{3sin(x)*-2cos(cos(x))*-sin(x)cos(cos(x))cos^{2}(x)}{xsin^{3}(cos(x))} + \frac{3sin(x)*-sin(cos(x))*-sin(x)cos^{2}(x)}{xsin^{2}(cos(x))} + \frac{3sin(x)cos(cos(x))*-2cos(x)sin(x)}{xsin^{2}(cos(x))} - \frac{6*-sin^{3}(x)cos(cos(x))}{x^{2}sin^{2}(cos(x))} - \frac{6*-2cos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))}{xsin^{3}(cos(x))} - \frac{6*3sin^{2}(x)cos(x)cos(cos(x))}{xsin^{2}(cos(x))} - \frac{6sin^{3}(x)*-sin(cos(x))*-sin(x)}{xsin^{2}(cos(x))} - \frac{3*-2cos^{2}(x)}{x^{3}sin(cos(x))} - \frac{3*-cos(cos(x))*-sin(x)cos^{2}(x)}{x^{2}sin^{2}(cos(x))} - \frac{3*-2cos(x)sin(x)}{x^{2}sin(cos(x))} + \frac{3*-sin^{3}(x)cos(x)}{x^{2}sin(cos(x))} + \frac{3*3sin^{2}(x)cos(x)cos(x)}{xsin(cos(x))} + \frac{3sin^{3}(x)*-cos(cos(x))*-sin(x)cos(x)}{xsin^{2}(cos(x))} + \frac{3sin^{3}(x)*-sin(x)}{xsin(cos(x))} + \frac{2*-3sin(x)cos(x)}{x^{4}sin(cos(x))} + \frac{2cos(x)cos(x)}{x^{3}sin(cos(x))} + \frac{2sin(x)*-cos(cos(x))*-sin(x)cos(x)}{x^{3}sin^{2}(cos(x))} + \frac{2sin(x)*-sin(x)}{x^{3}sin(cos(x))} - \frac{12*-sin(x)cos(x)}{x^{2}sin(cos(x))} - \frac{12cos(x)cos(x)}{xsin(cos(x))} - \frac{12sin(x)*-cos(cos(x))*-sin(x)cos(x)}{xsin^{2}(cos(x))} - \frac{12sin(x)*-sin(x)}{xsin(cos(x))} + \frac{3cos^{3}(x)cos(cos(x))}{(x)sin^{2}(cos(x))} + \frac{3ln(x)*-2cos(cos(x))*-sin(x)cos^{3}(x)cos(cos(x))}{sin^{3}(cos(x))} + \frac{3ln(x)*-3cos^{2}(x)sin(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{3ln(x)cos^{3}(x)*-sin(cos(x))*-sin(x)}{sin^{2}(cos(x))} + \frac{6sin^{2}(x)cos^{2}(cos(x))cos^{2}(x)}{(x)sin^{3}(cos(x))} + \frac{6ln(x)*-3cos(cos(x))*-sin(x)sin^{2}(x)cos^{2}(cos(x))cos^{2}(x)}{sin^{4}(cos(x))} + \frac{6ln(x)*2sin(x)cos(x)cos^{2}(cos(x))cos^{2}(x)}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos^{2}(x)}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(cos(x))*-2cos(x)sin(x)}{sin^{3}(cos(x))} + \frac{5sin^{4}(x)cos(cos(x))cos(x)}{(x)sin^{2}(cos(x))} + \frac{5ln(x)*-2cos(cos(x))*-sin(x)sin^{4}(x)cos(cos(x))cos(x)}{sin^{3}(cos(x))} + \frac{5ln(x)*4sin^{3}(x)cos(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} + \frac{5ln(x)sin^{4}(x)*-sin(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} + \frac{5ln(x)sin^{4}(x)cos(cos(x))*-sin(x)}{sin^{2}(cos(x))} - \frac{2sin^{2}(x)cos(cos(x))cos(x)}{(x)sin^{2}(cos(x))} - \frac{2ln(x)*2sin(x)cos(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{2ln(x)sin^{2}(x)*-2cos(cos(x))*-sin(x)cos(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{2ln(x)sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} - \frac{2ln(x)sin^{2}(x)cos(cos(x))*-sin(x)}{sin^{2}(cos(x))} + \frac{3*-2sin^{2}(x)}{x^{3}sin(cos(x))} + \frac{3*2sin(x)cos(x)}{x^{2}sin(cos(x))} + \frac{3sin^{2}(x)*-cos(cos(x))*-sin(x)}{x^{2}sin^{2}(cos(x))} - \frac{10sin^{2}(x)cos(x)cos(cos(x))}{(x)sin^{2}(cos(x))} - \frac{10ln(x)*2sin(x)cos(x)cos(x)cos(cos(x))}{sin^{2}(cos(x))} - \frac{10ln(x)sin^{2}(x)*-2cos(cos(x))*-sin(x)cos(x)cos(cos(x))}{sin^{3}(cos(x))} - \frac{10ln(x)sin^{2}(x)*-sin(x)cos(cos(x))}{sin^{2}(cos(x))} - \frac{10ln(x)sin^{2}(x)cos(x)*-sin(cos(x))*-sin(x)}{sin^{2}(cos(x))} + \frac{6sin^{2}(x)cos^{2}(x)cos^{2}(cos(x))}{(x)sin^{3}(cos(x))} + \frac{6ln(x)*2sin(x)cos(x)cos^{2}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{2}(x)*-3cos(cos(x))*-sin(x)cos^{2}(x)cos^{2}(cos(x))}{sin^{4}(cos(x))} + \frac{6ln(x)sin^{2}(x)*-2cos(x)sin(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{6ln(x)sin^{2}(x)cos^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{sin^{3}(cos(x))} + \frac{6sin^{4}(x)cos^{3}(cos(x))cos(x)}{(x)sin^{4}(cos(x))} + \frac{6ln(x)*-4cos(cos(x))*-sin(x)sin^{4}(x)cos^{3}(cos(x))cos(x)}{sin^{5}(cos(x))} + \frac{6ln(x)*4sin^{3}(x)cos(x)cos^{3}(cos(x))cos(x)}{sin^{4}(cos(x))} + \frac{6ln(x)sin^{4}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)cos(x)}{sin^{4}(cos(x))} + \frac{6ln(x)sin^{4}(x)cos^{3}(cos(x))*-sin(x)}{sin^{4}(cos(x))} - \frac{4sin^{2}(x)cos(cos(x))cos(x)}{(x)sin^{2}(cos(x))} - \frac{4ln(x)*-2cos(cos(x))*-sin(x)sin^{2}(x)cos(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{4ln(x)*2sin(x)cos(x)cos(cos(x))cos(x)}{sin^{2}(cos(x))} - \frac{4ln(x)sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x)}{sin^{2}(cos(x))} - \frac{4ln(x)sin^{2}(x)cos(cos(x))*-sin(x)}{sin^{2}(cos(x))} - \frac{6sin^{4}(x)cos^{2}(cos(x))}{(x)sin^{3}(cos(x))} - \frac{6ln(x)*4sin^{3}(x)cos(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} - \frac{6ln(x)sin^{4}(x)*-3cos(cos(x))*-sin(x)cos^{2}(cos(x))}{sin^{4}(cos(x))} - \frac{6ln(x)sin^{4}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{sin^{3}(cos(x))} - \frac{4cos^{2}(x)}{(x)sin(cos(x))} - \frac{4ln(x)*-cos(cos(x))*-sin(x)cos^{2}(x)}{sin^{2}(cos(x))} - \frac{4ln(x)*-2cos(x)sin(x)}{sin(cos(x))} + \frac{3sin^{2}(x)cos^{2}(x)}{(x)sin(cos(x))} + \frac{3ln(x)*-cos(cos(x))*-sin(x)sin^{2}(x)cos^{2}(x)}{sin^{2}(cos(x))} + \frac{3ln(x)*2sin(x)cos(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)*-2cos(x)sin(x)}{sin(cos(x))} + \frac{3sin^{2}(x)cos^{2}(x)}{(x)sin(cos(x))} + \frac{3ln(x)*2sin(x)cos(x)cos^{2}(x)}{sin(cos(x))} + \frac{3ln(x)sin^{2}(x)*-cos(cos(x))*-sin(x)cos^{2}(x)}{sin^{2}(cos(x))} + \frac{3ln(x)sin^{2}(x)*-2cos(x)sin(x)}{sin(cos(x))} + \frac{4sin^{2}(x)}{(x)sin(cos(x))} + \frac{4ln(x)*2sin(x)cos(x)}{sin(cos(x))} + \frac{4ln(x)sin^{2}(x)*-cos(cos(x))*-sin(x)}{sin^{2}(cos(x))} - \frac{3sin^{4}(x)}{(x)sin(cos(x))} - \frac{3ln(x)*4sin^{3}(x)cos(x)}{sin(cos(x))} - \frac{3ln(x)sin^{4}(x)*-cos(cos(x))*-sin(x)}{sin^{2}(cos(x))}\\=&\frac{8sin^{2}(x)cos(cos(x))cos(x)}{x^{3}sin^{2}(cos(x))} - \frac{12sin^{3}(x)cos^{2}(cos(x))cos(x)}{x^{2}sin^{3}(cos(x))} - \frac{12sin(x)cos^{2}(x)cos(cos(x))}{x^{2}sin^{2}(cos(x))} + \frac{20sin^{4}(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} - \frac{40sin^{2}(x)cos(x)cos(cos(x))}{xsin^{2}(cos(x))} + \frac{24sin^{2}(x)cos^{2}(x)cos^{2}(cos(x))}{xsin^{3}(cos(x))} + \frac{24sin^{4}(x)cos^{3}(cos(x))cos(x)}{xsin^{4}(cos(x))} - \frac{8sin^{2}(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} + \frac{24sin^{2}(x)cos^{2}(cos(x))cos^{2}(x)}{xsin^{3}(cos(x))} + \frac{12cos^{3}(x)cos(cos(x))}{xsin^{2}(cos(x))} - \frac{6sin(x)cos(cos(x))cos^{2}(x)}{x^{2}sin^{2}(cos(x))} - \frac{16sin^{2}(x)cos(cos(x))cos(x)}{xsin^{2}(cos(x))} + \frac{12sin^{2}(x)cos^{2}(x)}{xsin(cos(x))} - \frac{6sin^{3}(x)cos(x)}{x^{2}sin(cos(x))} - \frac{24sin^{4}(x)cos^{2}(cos(x))}{xsin^{3}(cos(x))} + \frac{12sin^{2}(x)cos^{2}(x)}{xsin(cos(x))} + \frac{8cos^{2}(x)}{x^{3}sin(cos(x))} - \frac{6sin(x)cos(x)}{x^{4}sin(cos(x))} + \frac{24sin(x)cos(x)}{x^{2}sin(cos(x))} - \frac{16cos^{2}(x)}{xsin(cos(x))} + \frac{12sin^{3}(x)cos(cos(x))}{x^{2}sin^{2}(cos(x))} - \frac{12sin^{4}(x)}{xsin(cos(x))} - \frac{8sin^{2}(x)}{x^{3}sin(cos(x))} + \frac{16sin^{2}(x)}{xsin(cos(x))} + \frac{6ln(x)sin(x)cos^{2}(cos(x))cos^{3}(x)}{sin^{3}(cos(x))} + \frac{24ln(x)sin(x)cos^{3}(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{18ln(x)sin^{3}(x)cos^{3}(cos(x))cos^{2}(x)}{sin^{4}(cos(x))} + \frac{28ln(x)sin^{5}(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} + \frac{20ln(x)sin^{3}(x)cos^{2}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{15ln(x)sin^{3}(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} - \frac{36ln(x)sin^{3}(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{41ln(x)sin(x)cos^{2}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{15ln(x)sin^{3}(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} - \frac{36ln(x)sin^{3}(x)cos(x)cos^{2}(cos(x))}{sin^{3}(cos(x))} + \frac{18ln(x)sin^{3}(x)cos^{3}(cos(x))cos^{2}(x)}{sin^{4}(cos(x))} + \frac{24ln(x)sin^{3}(x)cos^{2}(x)cos^{3}(cos(x))}{sin^{4}(cos(x))} + \frac{24ln(x)sin^{5}(x)cos^{4}(cos(x))cos(x)}{sin^{5}(cos(x))} - \frac{8ln(x)sin^{3}(x)cos^{2}(cos(x))cos(x)}{sin^{3}(cos(x))} - \frac{4ln(x)sin(x)cos(cos(x))cos^{2}(x)}{sin^{2}(cos(x))} - \frac{20ln(x)sin^{5}(x)cos(cos(x))}{sin^{2}(cos(x))} + \frac{5ln(x)sin^{5}(x)cos(x)}{sin(cos(x))} + \frac{12ln(x)sin^{3}(x)cos(cos(x))}{sin^{2}(cos(x))} - \frac{24ln(x)sin^{5}(x)cos^{3}(cos(x))}{sin^{4}(cos(x))} - \frac{22ln(x)sin^{3}(x)cos(x)}{sin(cos(x))} + \frac{8ln(x)sin^{3}(x)cos(cos(x))}{sin^{2}(cos(x))} - \frac{18ln(x)sin^{3}(x)cos(x)}{sin(cos(x))} + \frac{12ln(x)sin(x)cos^{3}(x)}{sin(cos(x))} + \frac{16ln(x)sin(x)cos(x)}{sin(cos(x))} + \frac{3ln(x)sin(x)cos^{3}(x)}{sin(cos(x))}\\ \end{split}\end{equation} \]