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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(sin(x))}^{cos(x)}e^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {sin(x)}^{cos(x)}e^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {sin(x)}^{cos(x)}e^{x}\right)}{dx}\\=&({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x} + {sin(x)}^{cos(x)}e^{x}\\=&-{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) + \frac{{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + {sin(x)}^{cos(x)}e^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) + \frac{{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + {sin(x)}^{cos(x)}e^{x}\right)}{dx}\\=&-({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))sin(x) - {sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - \frac{{sin(x)}^{cos(x)}e^{x}cos(x)sin(x)}{(sin(x))} - {sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) + \frac{({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{2}(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-2cos(x)sin(x)}{sin(x)} + ({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x} + {sin(x)}^{cos(x)}e^{x}\\=&{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - 3{sin(x)}^{cos(x)}e^{x}cos(x) - {sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) + \frac{{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} - \frac{{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} + {sin(x)}^{cos(x)}e^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - 3{sin(x)}^{cos(x)}e^{x}cos(x) - {sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) + \frac{{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} - \frac{{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} + {sin(x)}^{cos(x)}e^{x}\right)}{dx}\\=&({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln^{2}(sin(x))sin^{2}(x) + {sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) + \frac{{sin(x)}^{cos(x)}e^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + {sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))*2sin(x)cos(x) - 2({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))cos^{2}(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - \frac{2{sin(x)}^{cos(x)}e^{x}cos(x)cos^{2}(x)}{(sin(x))} - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))*-2cos(x)sin(x) - 2({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))sin(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - \frac{2{sin(x)}^{cos(x)}e^{x}cos(x)sin(x)}{(sin(x))} - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - 3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos(x) - 3{sin(x)}^{cos(x)}e^{x}cos(x) - 3{sin(x)}^{cos(x)}e^{x}*-sin(x) - ({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))cos(x) - {sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - \frac{{sin(x)}^{cos(x)}e^{x}cos(x)cos(x)}{(sin(x))} - {sin(x)}^{cos(x)}e^{x}ln(sin(x))*-sin(x) + \frac{({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} + \frac{2({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{2}(x)}{sin(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}*-2cos(x)sin(x)}{sin(x)} - \frac{({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{cos(x)}e^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{{sin(x)}^{cos(x)}e^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)} + ({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x} + {sin(x)}^{cos(x)}e^{x}\\=&3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 9{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x)cos(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos(x) - \frac{3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{4}(x)}{sin(x)} + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) - {sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{3}(x) - 6{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - \frac{9{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin(x)} - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - 9{sin(x)}^{cos(x)}e^{x}cos(x) - 3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{3}(x)} + \frac{5{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{3{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{3}(x)} + 3{sin(x)}^{cos(x)}e^{x}sin(x) + {sin(x)}^{cos(x)}e^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 9{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x)cos(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos(x) - \frac{3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{4}(x)}{sin(x)} + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) - {sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{3}(x) - 6{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - \frac{9{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin(x)} - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - 9{sin(x)}^{cos(x)}e^{x}cos(x) - 3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{3}(x)} + \frac{5{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{3{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{3}(x)} + 3{sin(x)}^{cos(x)}e^{x}sin(x) + {sin(x)}^{cos(x)}e^{x}\right)}{dx}\\=&3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{3{sin(x)}^{cos(x)}e^{x}*2ln(sin(x))cos(x)sin(x)cos^{2}(x)}{(sin(x))} + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))cos(x)cos^{2}(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)*-2cos(x)sin(x) + 9({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))sin(x)cos(x) + 9{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x)cos(x) + \frac{9{sin(x)}^{cos(x)}e^{x}cos(x)sin(x)cos(x)}{(sin(x))} + 9{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x)cos(x) + 9{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x)*-sin(x) + 3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln^{2}(sin(x))sin(x)cos(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos(x) + \frac{3{sin(x)}^{cos(x)}e^{x}*2ln(sin(x))cos(x)sin(x)cos(x)}{(sin(x))} + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))cos(x)cos(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)*-sin(x) - \frac{3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}cos(x)cos^{4}(x)}{(sin(x))sin(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}ln(sin(x))*-cos(x)cos^{4}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}ln(sin(x))*-4cos^{3}(x)sin(x)}{sin(x)} + 3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln^{2}(sin(x))sin^{2}(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) + \frac{3{sin(x)}^{cos(x)}e^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))*2sin(x)cos(x) - ({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln^{3}(sin(x))sin^{3}(x) - {sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{3}(x) - \frac{{sin(x)}^{cos(x)}e^{x}*3ln^{2}(sin(x))cos(x)sin^{3}(x)}{(sin(x))} - {sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))*3sin^{2}(x)cos(x) - 6({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))cos^{2}(x) - 6{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - \frac{6{sin(x)}^{cos(x)}e^{x}cos(x)cos^{2}(x)}{(sin(x))} - 6{sin(x)}^{cos(x)}e^{x}ln(sin(x))*-2cos(x)sin(x) - \frac{9({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{3}(x)}{sin(x)} - \frac{9{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin(x)} - \frac{9{sin(x)}^{cos(x)}e^{x}*-cos(x)cos^{3}(x)}{sin^{2}(x)} - \frac{9{sin(x)}^{cos(x)}e^{x}*-3cos^{2}(x)sin(x)}{sin(x)} - 2({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))sin(x) - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x) - \frac{2{sin(x)}^{cos(x)}e^{x}cos(x)sin(x)}{(sin(x))} - 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - 9({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos(x) - 9{sin(x)}^{cos(x)}e^{x}cos(x) - 9{sin(x)}^{cos(x)}e^{x}*-sin(x) - 3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}ln(sin(x))cos(x) - 3{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) - \frac{3{sin(x)}^{cos(x)}e^{x}cos(x)cos(x)}{(sin(x))} - 3{sin(x)}^{cos(x)}e^{x}ln(sin(x))*-sin(x) - \frac{3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{5}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}*-3cos(x)cos^{5}(x)}{sin^{4}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}*-5cos^{4}(x)sin(x)}{sin^{3}(x)} + \frac{5({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{2}(x)}{sin(x)} + \frac{5{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} + \frac{5{sin(x)}^{cos(x)}e^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{5{sin(x)}^{cos(x)}e^{x}*-2cos(x)sin(x)}{sin(x)} + \frac{({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-3cos(x)cos^{6}(x)}{sin^{4}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}*-6cos^{5}(x)sin(x)}{sin^{3}(x)} + \frac{3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{cos(x)}e^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{3{sin(x)}^{cos(x)}e^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - \frac{3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{cos(x)}e^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)} + \frac{2({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}cos^{4}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}*-3cos(x)cos^{4}(x)}{sin^{4}(x)} + \frac{2{sin(x)}^{cos(x)}e^{x}*-4cos^{3}(x)sin(x)}{sin^{3}(x)} + 3({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x}sin(x) + 3{sin(x)}^{cos(x)}e^{x}sin(x) + 3{sin(x)}^{cos(x)}e^{x}cos(x) + ({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))e^{x} + {sin(x)}^{cos(x)}e^{x}\\=&-4{sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{2}(x)cos^{2}(x) + 6{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))cos^{4}(x) + 12{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 36{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{3}(x) + 6{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))cos^{3}(x) - 18{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x)cos(x) + 36{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin(x)cos(x) + 39{sin(x)}^{cos(x)}e^{x}cos^{2}(x) + 2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{2}(x) - 6{sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{2}(x)cos(x) + 12{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin(x)cos(x) + 3{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))cos^{2}(x) - \frac{4{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{6}(x)}{sin^{2}(x)} - \frac{12{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{18{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{5}(x)}{sin^{2}(x)} - \frac{2{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos^{4}(x)}{sin^{2}(x)} + {sin(x)}^{cos(x)}e^{x}ln^{4}(sin(x))sin^{4}(x) - 12{sin(x)}^{cos(x)}e^{x}ln(sin(x))sin^{2}(x) - \frac{36{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin(x)} + \frac{32{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{2}(x)} + 2{sin(x)}^{cos(x)}e^{x}ln^{2}(sin(x))sin^{2}(x) - 18{sin(x)}^{cos(x)}e^{x}cos(x) - 5{sin(x)}^{cos(x)}e^{x}ln(sin(x))cos(x) + \frac{11{sin(x)}^{cos(x)}e^{x}cos^{6}(x)}{sin^{4}(x)} + \frac{12{sin(x)}^{cos(x)}e^{x}cos^{2}(x)}{sin(x)} - \frac{6{sin(x)}^{cos(x)}e^{x}cos^{7}(x)}{sin^{4}(x)} - \frac{12{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{3}(x)} - \frac{16{sin(x)}^{cos(x)}e^{x}cos^{3}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{cos(x)}e^{x}cos^{8}(x)}{sin^{4}(x)} + \frac{4{sin(x)}^{cos(x)}e^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{8{sin(x)}^{cos(x)}e^{x}cos^{4}(x)}{sin^{3}(x)} - \frac{6{sin(x)}^{cos(x)}e^{x}cos^{5}(x)}{sin^{4}(x)} - 4{sin(x)}^{cos(x)}e^{x}ln^{3}(sin(x))sin^{3}(x) + 12{sin(x)}^{cos(x)}e^{x}sin(x) + {sin(x)}^{cos(x)}e^{x}\\ \end{split}\end{equation} \]