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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arctan(sin(cos(ln(x))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(sin(cos(ln(x))))\right)}{dx}\\=&(\frac{(\frac{cos(cos(ln(x)))*-sin(ln(x))}{(x)})}{(1 + (sin(cos(ln(x))))^{2})})\\=&\frac{-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x}\right)}{dx}\\=&\frac{-(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(ln(x))cos(cos(ln(x)))}{x} - \frac{-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x(x)}\\=&\frac{-2sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{2}} + \frac{sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{2}} + \frac{sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}}\right)}{dx}\\=&\frac{-2(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{x^{2}} - \frac{2*-2sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{2*2sin(ln(x))cos(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{2}(x)} - \frac{2sin^{2}(ln(x))cos(cos(ln(x)))*-sin(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{2}(x)} - \frac{2sin^{2}(ln(x))sin(cos(ln(x)))*-2cos(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{2}(x)} + \frac{(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(ln(x))cos(cos(ln(x)))}{x^{2}} + \frac{-2sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)} + \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)} - \frac{(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})cos(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{-2cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} - \frac{-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)} - \frac{cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)} - \frac{(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(cos(ln(x)))sin^{2}(ln(x))}{x^{2}} - \frac{-2sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} - \frac{cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)} - \frac{sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{2}(x)}\\=& - \frac{4sin(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{2sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{8sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{3}} + \frac{2sin^{3}(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{4sin^{2}(cos(ln(x)))sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{6sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{2sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{4sin(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{2sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{8sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{3}} + \frac{2sin^{3}(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{4sin^{2}(cos(ln(x)))sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{6sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} - \frac{2sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}}\right)}{dx}\\=& - \frac{4(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{x^{3}} - \frac{4*-3sin(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{4cos(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4sin(ln(x))cos(cos(ln(x)))*-sin(ln(x))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4sin(ln(x))sin(cos(ln(x)))*-sin(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4sin(ln(x))sin(cos(ln(x)))cos(ln(x))*-2cos(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{x^{3}} - \frac{2*-3sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{2cos(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2sin(ln(x))cos(cos(ln(x)))*-sin(ln(x))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2sin(ln(x))sin(cos(ln(x)))*-2cos(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{8(\frac{-3(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{4}})sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{x^{3}} - \frac{8*-3sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} - \frac{8*3sin^{2}(ln(x))cos(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{3}(x)} - \frac{8sin^{3}(ln(x))*2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{3}(x)} - \frac{8sin^{3}(ln(x))sin^{2}(cos(ln(x)))*-3cos^{2}(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{3}(x)} + \frac{2(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin^{3}(ln(x))cos^{3}(cos(ln(x)))}{x^{3}} + \frac{2*-3sin^{3}(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{2*3sin^{2}(ln(x))cos(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} + \frac{2sin^{3}(ln(x))*-3cos^{2}(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin^{2}(cos(ln(x)))sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{4*-3sin^{2}(cos(ln(x)))sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{4*2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4sin^{2}(cos(ln(x)))*3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{4sin^{2}(cos(ln(x)))sin^{3}(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{-3sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{3(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})cos(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{3*-3cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{3*-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{3cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} - \frac{3(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{3}} - \frac{3*-3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{3cos(cos(ln(x)))*-sin(ln(x))sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} - \frac{3sin(cos(ln(x)))cos(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} - \frac{3sin(cos(ln(x)))sin(ln(x))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{6(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{x^{3}} + \frac{6*-3sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{6*2sin(ln(x))cos(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} + \frac{6sin^{2}(ln(x))cos(cos(ln(x)))*-sin(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} + \frac{6sin^{2}(ln(x))sin(cos(ln(x)))*-2cos(cos(ln(x)))sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2(\frac{-2(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{3}})sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{x^{3}} - \frac{2*-3sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{2*3sin^{2}(ln(x))cos(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2sin^{3}(ln(x))*2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} - \frac{2sin^{3}(ln(x))sin^{2}(cos(ln(x)))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{3}(x)} + \frac{3(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} + \frac{3*-3sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{3cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{3sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{(\frac{-(\frac{2sin(cos(ln(x)))cos(cos(ln(x)))*-sin(ln(x))}{(x)} + 0)}{(sin^{2}(cos(ln(x))) + 1)^{2}})sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{-3sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)} + \frac{sin^{3}(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{3}(x)}\\=& - \frac{24sin^{2}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} + \frac{24sin(ln(x))sin(cos(ln(x)))cos(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{6sin(cos(ln(x)))cos^{2}(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{6sin^{2}(ln(x))cos^{3}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{20sin^{2}(cos(ln(x)))sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{12sin(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{4sin^{2}(cos(ln(x)))sin^{2}(ln(x))cos(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{6sin^{2}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{24sin^{2}(ln(x))sin^{2}(cos(ln(x)))cos(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} - \frac{6sin^{2}(ln(x))sin^{2}(cos(ln(x)))cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{48sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} + \frac{16sin(cos(ln(x)))sin^{4}(ln(x))cos^{4}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} - \frac{24sin^{3}(cos(ln(x)))sin^{4}(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} + \frac{8sin^{4}(ln(x))sin(cos(ln(x)))cos^{4}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} + \frac{6sin^{2}(ln(x))cos(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{48sin^{4}(ln(x))sin^{3}(cos(ln(x)))cos^{4}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{4}x^{4}} - \frac{24sin^{4}(ln(x))sin^{3}(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{3}x^{4}} + \frac{24sin^{2}(cos(ln(x)))sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{10cos(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{14sin^{2}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{3sin^{2}(ln(x))cos(cos(ln(x)))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{18sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{12sin^{3}(ln(x))sin^{2}(cos(ln(x)))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{12sin^{3}(ln(x))cos^{3}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{3sin(cos(ln(x)))cos^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} + \frac{18sin(cos(ln(x)))sin^{4}(ln(x))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{2sin^{4}(ln(x))sin(cos(ln(x)))cos^{2}(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} - \frac{7sin(cos(ln(x)))sin^{2}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{6sin^{3}(ln(x))cos(cos(ln(x)))}{(sin^{2}(cos(ln(x))) + 1)x^{4}} - \frac{6sin^{3}(cos(ln(x)))sin^{4}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)^{2}x^{4}} + \frac{sin(cos(ln(x)))sin^{4}(ln(x))}{(sin^{2}(cos(ln(x))) + 1)x^{4}}\\ \end{split}\end{equation} \]