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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(cos(arccos(sin(x))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(cos(arccos(sin(x))))\right)}{dx}\\=&cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})\\=&\frac{sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x)))) + \frac{cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))*-sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))cos(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{sin(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{5}{2}}})sin(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x)))) + \frac{cos(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(x)cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(x)sin(arccos(sin(x)))*-2cos(x)sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(x)sin(arccos(sin(x)))cos^{2}(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{-2cos(x)sin(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{cos^{2}(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{cos^{2}(x)cos(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x)))) - \frac{cos(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(x)cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(x)sin(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{2sin(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{2}(arccos(sin(x)))cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))*-2cos(x)sin(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{3sin^{2}(x)sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{2sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin^{2}(x)sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{2sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} + \frac{sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{2sin(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{2}} + \frac{2sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{3}(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3sin^{2}(x)sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{2sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin^{2}(x)sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{2sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} + \frac{sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{2sin(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{2}} + \frac{2sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{3}(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{7}{2}}})sin^{2}(x)sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x)))) + \frac{3*2sin(x)cos(x)sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{3sin^{2}(x)cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{3sin^{2}(x)sin(arccos(sin(x)))*-3cos^{2}(x)sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{3sin^{2}(x)sin(arccos(sin(x)))cos^{3}(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + 2(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x)))) + \frac{2cos(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} + \frac{2sin(x)*-sin(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} + \frac{2sin(x)cos(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} + \frac{2sin(x)cos(x)cos(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{5}{2}}})sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{cos(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin(x)*-3cos^{2}(x)sin(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin(x)cos^{3}(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin(x)cos^{3}(x)cos(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - 3(\frac{\frac{-3}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{5}{2}}})sin^{2}(x)sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x)))) - \frac{3*2sin(x)cos(x)sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin^{2}(x)cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin^{2}(x)sin(arccos(sin(x)))*-sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin^{2}(x)sin(arccos(sin(x)))cos(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{5}{2}}})sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{2sin(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin^{2}(arccos(sin(x)))cos(x)sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(x)cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))*-3cos^{2}(x)sin(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - 2(\frac{-2(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{3}})sin(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x)))) - \frac{2cos(x)cos^{3}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)*-3cos^{2}(x)sin(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)cos^{3}(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)cos^{3}(x)cos(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{2}} + (\frac{\frac{-3}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{5}{2}}})sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x)))) + \frac{cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(arccos(sin(x)))*-3cos^{2}(x)sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin(arccos(sin(x)))cos^{3}(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{cos(x)cos(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(x)*-sin(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(x)cos(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(x)cos(x)cos(arccos(sin(x)))*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)} + \frac{cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(cos(arccos(sin(x))))cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))sin(cos(arccos(sin(x))))*-3cos^{2}(x)sin(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(arccos(sin(x)))cos(x)cos(cos(arccos(sin(x)))) - \frac{cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))*-sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))*-3cos^{2}(x)sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin(arccos(sin(x)))cos^{3}(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{2}(arccos(sin(x)))cos(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{2}(arccos(sin(x)))sin(x)cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))*-sin(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - 2(\frac{-2(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{3}})sin(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x) - \frac{2cos(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)*2sin(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(cos(arccos(sin(x))))cos^{3}(x)}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)sin^{2}(arccos(sin(x)))cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)}{(-sin^{2}(x) + 1)^{2}} - \frac{2sin(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))*-3cos^{2}(x)sin(x)}{(-sin^{2}(x) + 1)^{2}} + \frac{2(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)} + \frac{2cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin(arccos(sin(x)))cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(arccos(sin(x)))cos^{3}(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin(arccos(sin(x)))sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos(arccos(sin(x)))*-3cos^{2}(x)sin(x)}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin^{3}(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}})sin^{3}(arccos(sin(x)))cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{3sin^{2}(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos^{3}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{3}(arccos(sin(x)))*-3cos^{2}(x)sin(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{3}(arccos(sin(x)))cos^{3}(x)*-sin(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + 2(\frac{-(-2sin(x)cos(x) + 0)}{(-sin^{2}(x) + 1)^{2}})sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(x) + \frac{2*2sin(arccos(sin(x)))cos(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})sin(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)} + \frac{2sin^{2}(arccos(sin(x)))cos(x)sin(cos(arccos(sin(x))))cos(x)}{(-sin^{2}(x) + 1)} + \frac{2sin^{2}(arccos(sin(x)))sin(x)cos(cos(arccos(sin(x))))*-sin(arccos(sin(x)))(\frac{-(cos(x))}{((1 - (sin(x))^{2})^{\frac{1}{2}})})cos(x)}{(-sin^{2}(x) + 1)} + \frac{2sin^{2}(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))*-sin(x)}{(-sin^{2}(x) + 1)}\\=&\frac{15sin^{3}(x)sin(arccos(sin(x)))cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{7}{2}}} + \frac{6sin(x)sin(arccos(sin(x)))cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sin^{2}(x)cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{5}{2}}} - \frac{18sin^{3}(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} - \frac{6sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{2}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)} + \frac{15sin^{2}(x)cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} + \frac{3cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{7sin(x)sin(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{2sin(arccos(sin(x)))sin(x)cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)} - \frac{3sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{2}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{12sin^{2}(x)cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{3}} - \frac{3cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}} - \frac{sin(arccos(sin(x)))sin(x)cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{3sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{4}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{2}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{3sin^{2}(x)cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin(x)sin^{3}(arccos(sin(x)))cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} + \frac{2sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{4}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{2}} + \frac{4sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{2}} + \frac{sin(arccos(sin(x)))sin(x)cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{sin^{3}(arccos(sin(x)))sin(x)cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{2}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{9sin(x)sin(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sin^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)} - \frac{2sin(arccos(sin(x)))sin(x)cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{2}} + \frac{3sin^{2}(arccos(sin(x)))sin^{2}(x)sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sin^{3}(arccos(sin(x)))sin(x)cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{2sin^{3}(arccos(sin(x)))sin(x)cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)} - \frac{3sin^{2}(arccos(sin(x)))sin^{2}(x)sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos^{2}(x)cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sin^{2}(arccos(sin(x)))cos^{4}(x)cos(cos(arccos(sin(x))))cos(arccos(sin(x)))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{3sin^{2}(arccos(sin(x)))cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{6sin(arccos(sin(x)))sin(x)sin(cos(arccos(sin(x))))cos(arccos(sin(x)))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{cos^{2}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{3sin(x)sin^{3}(arccos(sin(x)))cos^{2}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{2sin^{3}(arccos(sin(x)))sin(x)cos^{4}(x)cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{2}} + \frac{cos^{4}(x)cos(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{4sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{6sin^{2}(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{2}} + \frac{3sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)} - \frac{sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sin(cos(arccos(sin(x))))sin^{2}(arccos(sin(x)))sin^{2}(x)cos^{2}(x)}{(-sin^{2}(x) + 1)^{2}} - \frac{12sin^{2}(x)sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{3}} + \frac{sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{2}(x)}{(-sin^{2}(x) + 1)^{\frac{1}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{6sin(cos(arccos(sin(x))))sin^{2}(x)sin^{2}(arccos(sin(x)))cos^{2}(x)}{(-sin^{2}(x) + 1)^{2}} - \frac{3sin(cos(arccos(sin(x))))sin^{2}(arccos(sin(x)))sin^{2}(x)}{(-sin^{2}(x) + 1)} + \frac{3sin^{3}(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sin(cos(arccos(sin(x))))cos^{2}(arccos(sin(x)))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin(x)sin(arccos(sin(x)))cos(cos(arccos(sin(x))))}{(-sin^{2}(x) + 1)^{\frac{1}{2}}} + \frac{sin^{4}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{\frac{3}{2}}(-sin^{2}(x) + 1)^{\frac{1}{2}}} - \frac{3sin^{2}(arccos(sin(x)))sin(cos(arccos(sin(x))))cos^{4}(x)}{(-sin^{2}(x) + 1)^{2}}\\ \end{split}\end{equation} \]