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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{cos(x)}^{sin(x)}}^{cos(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{cos(x)}^{sin(x)}}^{cos(x)}\right)}{dx}\\=&({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))\\=&-{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}sin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}sin^{2}(x)\right)}{dx}\\=&-({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin(x)}{({cos(x)}^{sin(x)})} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})cos(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)cos^{2}(x)}{(cos(x))} + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*-2cos(x)sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}*2sin(x)cos(x)\\=&-3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x)cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)}{cos(x)} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin(x)cos^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))cos^{4}(x) + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{3}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}sin(x)cos(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x)cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)}{cos(x)} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin(x)cos^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))cos^{4}(x) + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{3}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}sin(x)cos(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x)\right)}{dx}\\=&-3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin(x)cos(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin(x)cos(x)}{(cos(x))} - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos(x)cos(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)*-sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x)}{(cos(x))} - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} - {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})cos(x)cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin(x)*-2cos(x)sin(x) - 2({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin^{2}(x)cos^{2}(x) - \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin^{2}(x)cos^{2}(x)}{(cos(x))} - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*2sin(x)cos(x)cos^{2}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x)*-2cos(x)sin(x) + \frac{({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{3}(x)}{cos(x)} + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*3sin^{2}(x)cos(x)}{cos(x)} + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)sin(x)}{cos^{2}(x)} - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})cos(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))cos(x)}{({cos(x)}^{sin(x)})} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*-sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})ln(cos(x))sin(x)cos^{2}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln(cos(x))sin(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*-sin(x)sin(x)cos^{2}(x)}{(cos(x))} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))cos(x)cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin(x)*-2cos(x)sin(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}(cos(x))cos^{4}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*2ln(cos(x))*-sin(x)cos^{4}(x)}{(cos(x))} + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))*-4cos^{3}(x)sin(x) + 2({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin^{3}(x) + \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{3}(x)}{({cos(x)}^{sin(x)})} + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*3sin^{2}(x)cos(x) - 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin(x)cos(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}cos(x)cos(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}sin(x)*-sin(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*2ln({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{2}(x)}{({cos(x)}^{sin(x)})} + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})*2sin(x)cos(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{4}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}*4sin^{3}(x)cos(x)\\=&5{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos(x) - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin(x)cos^{3}(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{3}(x)cos(x) + 9{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)cos(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos^{2}(x) + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos^{2}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x)cos^{2}(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))cos^{3}(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)cos^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{2}(x)cos^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{4}(x)cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x)}{cos^{2}(x)} - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)cos^{3}(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{4}(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}sin^{5}(x)}{cos(x)} + 10{{cos(x)}^{sin(x)}}^{cos(x)}sin^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin(x)cos(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})cos^{3}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin(x)cos^{4}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))cos^{6}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})sin^{3}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)cos^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{5}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin(x) - {{cos(x)}^{sin(x)}}^{cos(x)}sin^{6}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 5{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos(x) - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin(x)cos^{3}(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{3}(x)cos(x) + 9{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)cos(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos^{2}(x) + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos^{2}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x)cos^{2}(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))cos^{3}(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)cos^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{2}(x)cos^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{4}(x)cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x)}{cos^{2}(x)} - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)cos^{3}(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{4}(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}sin^{5}(x)}{cos(x)} + 10{{cos(x)}^{sin(x)}}^{cos(x)}sin^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin(x)cos(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})cos^{3}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin(x)cos^{4}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))cos^{6}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{4}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}cos^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})sin^{3}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)cos^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{5}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin(x) - {{cos(x)}^{sin(x)}}^{cos(x)}sin^{6}(x)\right)}{dx}\\=&5({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos(x) + \frac{5{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln(cos(x))sin^{2}(x)cos(x)}{({cos(x)}^{sin(x)})} + \frac{5{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*-sin(x)sin^{2}(x)cos(x)}{(cos(x))} + 5{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))*2sin(x)cos(x)cos(x) + 5{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)*-sin(x) - 9({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}(cos(x))sin(x)cos^{3}(x) - \frac{9{{cos(x)}^{sin(x)}}^{cos(x)}*2ln(cos(x))*-sin(x)sin(x)cos^{3}(x)}{(cos(x))} - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))cos(x)cos^{3}(x) - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin(x)*-3cos^{2}(x)sin(x) + 12({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin^{3}(x)cos(x) + \frac{12{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin^{3}(x)cos(x)}{(cos(x))} + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*3sin^{2}(x)cos(x)cos(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{3}(x)*-sin(x) + 9({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{3}(x)cos(x) + 9{{cos(x)}^{sin(x)}}^{cos(x)}*3sin^{2}(x)cos(x)cos(x) + 9{{cos(x)}^{sin(x)}}^{cos(x)}sin^{3}(x)*-sin(x) - 4({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))cos^{2}(x) - \frac{4{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)cos^{2}(x)}{(cos(x))} - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*-2cos(x)sin(x) + 2({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos^{2}(x) + \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}*2ln({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln(cos(x))sin^{2}(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} + \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})*-sin(x)sin^{2}(x)cos^{2}(x)}{(cos(x))} + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))*2sin(x)cos(x)cos^{2}(x) + 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)*-2cos(x)sin(x) - 2({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{4}(x) - \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}*2ln(cos(x))*-sin(x)ln({cos(x)}^{sin(x)})sin(x)cos^{4}(x)}{(cos(x))} - \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin(x)cos^{4}(x)}{({cos(x)}^{sin(x)})} - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})cos(x)cos^{4}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin(x)*-4cos^{3}(x)sin(x) + 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x)cos^{2}(x) + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)ln({cos(x)}^{sin(x)})sin^{3}(x)cos^{2}(x)}{(cos(x))} + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{3}(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})*3sin^{2}(x)cos(x)cos^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x)*-2cos(x)sin(x) + 12({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) + \frac{12{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{2}(x)cos(x)}{({cos(x)}^{sin(x)})} + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*2sin(x)cos(x)cos(x) + 12{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{2}(x)*-sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})ln(cos(x))cos^{3}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln(cos(x))cos^{3}(x)}{({cos(x)}^{sin(x)})} - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*-sin(x)cos^{3}(x)}{(cos(x))} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))*-3cos^{2}(x)sin(x) + 4({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x) + \frac{4{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)ln({cos(x)}^{sin(x)})sin^{2}(x)cos(x)}{(cos(x))} + \frac{4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{2}(x)cos(x)}{({cos(x)}^{sin(x)})} + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})*2sin(x)cos(x)cos(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)*-sin(x) + 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)cos^{2}(x) + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln(cos(x))sin^{3}(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*-sin(x)sin^{3}(x)cos^{2}(x)}{(cos(x))} + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))*3sin^{2}(x)cos(x)cos^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)*-2cos(x)sin(x) - 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}(cos(x))sin^{2}(x)cos^{4}(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*2ln(cos(x))*-sin(x)sin^{2}(x)cos^{4}(x)}{(cos(x))} - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))*2sin(x)cos(x)cos^{4}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{2}(x)*-4cos^{3}(x)sin(x) + 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin^{4}(x)cos^{2}(x) + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin^{4}(x)cos^{2}(x)}{(cos(x))} + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*4sin^{3}(x)cos(x)cos^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{4}(x)*-2cos(x)sin(x) + \frac{({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{4}(x)}{cos^{2}(x)} + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*4sin^{3}(x)cos(x)}{cos^{2}(x)} + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x)*2sin(x)}{cos^{3}(x)} - 9({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin(x)cos^{3}(x) - \frac{9{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin(x)cos^{3}(x)}{(cos(x))} - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos(x)cos^{3}(x) - 9{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)*-3cos^{2}(x)sin(x) - \frac{3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin^{4}(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{4}(x)}{({cos(x)}^{sin(x)})cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*4sin^{3}(x)cos(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{4}(x)sin(x)}{cos^{2}(x)} - \frac{3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{5}(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*5sin^{4}(x)cos(x)}{cos(x)} - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}sin^{5}(x)sin(x)}{cos^{2}(x)} + 10({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{2}(x) + 10{{cos(x)}^{sin(x)}}^{cos(x)}*2sin(x)cos(x) + 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}({cos(x)}^{sin(x)})sin(x)cos(x) + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*2ln({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin(x)cos(x)}{({cos(x)}^{sin(x)})} + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})cos(x)cos(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin(x)*-sin(x) - 2({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))ln({cos(x)}^{sin(x)})cos^{3}(x) - \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)ln({cos(x)}^{sin(x)})cos^{3}(x)}{(cos(x))} - \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))cos^{3}(x)}{({cos(x)}^{sin(x)})} - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})*-3cos^{2}(x)sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin(x)cos^{4}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))ln^{2}(cos(x))sin(x)cos^{4}(x)}{({cos(x)}^{sin(x)})} - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*2ln(cos(x))*-sin(x)sin(x)cos^{4}(x)}{(cos(x))} - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))cos(x)cos^{4}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin(x)*-4cos^{3}(x)sin(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{3}(cos(x))cos^{6}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*3ln^{2}(cos(x))*-sin(x)cos^{6}(x)}{(cos(x))} + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))*-6cos^{5}(x)sin(x) - 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{2}({cos(x)}^{sin(x)})sin^{4}(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*2ln({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{4}(x)}{({cos(x)}^{sin(x)})} - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})*4sin^{3}(x)cos(x) + 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))sin^{2}(x) + \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)sin^{2}(x)}{(cos(x))} + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*2sin(x)cos(x) - 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))cos^{2}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}*-2cos(x)sin(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln^{3}({cos(x)}^{sin(x)})sin^{3}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*3ln^{2}({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{3}(x)}{({cos(x)}^{sin(x)})} - {{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})*3sin^{2}(x)cos(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)cos^{2}(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}*-sin(x)ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)cos^{2}(x)}{(cos(x))} + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))*2ln({cos(x)}^{sin(x)})({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{2}(x)cos^{2}(x)}{({cos(x)}^{sin(x)})} + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})*2sin(x)cos(x)cos^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)*-2cos(x)sin(x) - 3({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin^{5}(x) - \frac{3{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin^{5}(x)}{({cos(x)}^{sin(x)})} - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})*5sin^{4}(x)cos(x) + ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))ln({cos(x)}^{sin(x)})sin(x) + \frac{{{cos(x)}^{sin(x)}}^{cos(x)}({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))}))sin(x)}{({cos(x)}^{sin(x)})} + {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})cos(x) - ({{cos(x)}^{sin(x)}}^{cos(x)}((-sin(x))ln({cos(x)}^{sin(x)}) + \frac{(cos(x))(({cos(x)}^{sin(x)}((cos(x))ln(cos(x)) + \frac{(sin(x))(-sin(x))}{(cos(x))})))}{({cos(x)}^{sin(x)})}))sin^{6}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}*6sin^{5}(x)cos(x)\\=&-13{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)cos(x) + 23{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)cos^{3}(x) - 29{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{4}(x)cos(x) + 39{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{2}(x)cos^{2}(x) - 18{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))sin(x)cos^{5}(x) + 110{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{2}(x)cos^{2}(x) + 17{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin(x)cos^{2}(x) + 13{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin^{2}(x)cos^{3}(x) + 42{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{3}(x)cos^{3}(x) - 30{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{5}(x)cos(x) - 16{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))cos^{4}(x) + 36{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{3}(x)cos^{3}(x) + 39{{cos(x)}^{sin(x)}}^{cos(x)}sin^{2}(x)cos^{2}(x) + 30{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x) - 42{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{4}(x)cos(x) - 18{{cos(x)}^{sin(x)}}^{cos(x)}sin^{5}(x)cos(x) + \frac{2{{cos(x)}^{sin(x)}}^{cos(x)}sin^{5}(x)}{cos^{3}(x)} + 30{{cos(x)}^{sin(x)}}^{cos(x)}sin(x)cos(x) - 30{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{3}(x)cos(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x)cos^{2}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{2}(x)cos^{4}(x) - 8{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin^{4}(x)cos^{2}(x) + 7{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln(cos(x))sin(x)cos^{3}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})ln^{2}(cos(x))sin^{2}(x)cos^{4}(x) - 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{6}(x) + 8{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x)cos^{4}(x) + 27{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{2}(x)cos^{3}(x) - 2{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))cos^{5}(x) - 19{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{4}(x)cos(x) - 6{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{5}(x)cos^{2}(x) - 18{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin(x)cos^{5}(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}(cos(x))sin^{2}(x)cos^{6}(x) - \frac{{{cos(x)}^{sin(x)}}^{cos(x)}sin^{6}(x)}{cos^{2}(x)} - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))ln({cos(x)}^{sin(x)})cos^{5}(x) + 21{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{2}(x)cos^{3}(x) + 21{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin(x)cos^{2}(x) - 6{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{5}(x)cos^{2}(x) + 5{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin(x)cos^{3}(x) - 5{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{3}(x)cos(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{2}(cos(x))sin^{3}(x)cos^{4}(x) + 6{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}(cos(x))sin^{4}(x)cos^{4}(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{6}(x)cos^{2}(x) - \frac{4{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{5}(x)}{cos^{2}(x)} + 15{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin(x)cos(x) + \frac{12{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{6}(x)}{cos(x)} + \frac{6{{cos(x)}^{sin(x)}}^{cos(x)}sin^{7}(x)}{cos(x)} - 12{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))cos^{4}(x) + \frac{6{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{5}(x)}{cos(x)} - 58{{cos(x)}^{sin(x)}}^{cos(x)}sin^{4}(x) - 6{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})sin^{2}(x)cos(x) - 50{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{3}(x) + 3{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})cos^{2}(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{2}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln^{3}(cos(x))sin(x)cos^{6}(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{2}({cos(x)}^{sin(x)})sin^{4}(x)cos^{2}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{4}(cos(x))cos^{8}(x) - 26{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))sin^{4}(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln^{3}({cos(x)}^{sin(x)})sin^{5}(x) - {{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln^{3}({cos(x)}^{sin(x)})sin^{3}(x)cos^{2}(x) - 8{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})ln(cos(x))sin^{3}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln^{4}({cos(x)}^{sin(x)})sin^{4}(x) - 4{{cos(x)}^{sin(x)}}^{cos(x)}ln(cos(x))ln({cos(x)}^{sin(x)})sin^{3}(x) + 6{{cos(x)}^{sin(x)}}^{cos(x)}ln^{2}({cos(x)}^{sin(x)})sin^{6}(x) + 4{{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})sin^{7}(x) + {{cos(x)}^{sin(x)}}^{cos(x)}ln({cos(x)}^{sin(x)})cos(x) + {{cos(x)}^{sin(x)}}^{cos(x)}sin^{8}(x)\\ \end{split}\end{equation} \]