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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(x){\frac{1}{({a}^{(2 + {b}^{(2 - 2abcos(x))})} + 1)}}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}})sin(x) + \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\=&\frac{-ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x) - \frac{ab({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{ab{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*0ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)*0sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)*2sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + (\frac{\frac{-1}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}})cos(x) + \frac{-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\=& - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=& - 3(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)cos(x) - \frac{3ab({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln(a)ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*0ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)*0sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)cos(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)*-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 2(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{3}(x) - \frac{2a^{2}b^{2}({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{2}(b)ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*2ln(b)*0ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)*0sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{2a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)*3sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 2(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x) - \frac{2a^{2}b^{2}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*2ln(b)*0ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)*2ln(a)*0sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{2a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)*3sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + 3(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{3}(x) + \frac{3a^{2}b^{2}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*2ln(b)*0ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)*2ln(a)*0sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{3a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)*3sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - (\frac{\frac{-1}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}})sin(x) - \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\=&\frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{4ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{4ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&18(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x) + \frac{18a^{2}b^{2}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*2ln(b)*0ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)*2ln(a)*0sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)*2sin(x)cos(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{2}(x)*-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - 12(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{2}(x)cos(x) - \frac{12a^{2}b^{2}({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{2}(b)ln(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*2ln(b)*0ln(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)*0sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)*2sin(x)cos(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{2}(x)*-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 12(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x) - \frac{12a^{2}b^{2}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{2}(b)ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*2ln(b)*0ln^{2}(a)sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)*2ln(a)*0sin^{2}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)*2sin(x)cos(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)*-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 3(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)cos^{2}(x) - \frac{3ab({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})){b}^{(-2abcos(x) + 2)}ln(b)ln(a)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)}))ln(b)ln(a)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}*0ln(a)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)*0cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{3ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)*-2cos(x)sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 12(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)sin^{4}(x) - \frac{12a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*3ln^{2}(b)*0ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)*2ln(a)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + 6(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)sin^{4}(x) + \frac{6a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{2}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*2ln(a)*0ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)*3ln^{2}(b)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x) + \frac{6a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*3ln^{2}(a)*0ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)*3ln^{2}(b)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{6a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - 4(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)sin^{4}(x) - \frac{4a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*3ln^{2}(b)*0ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)*3ln^{2}(a)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{4a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 4(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)sin^{4}(x) - \frac{4a^{3}b^{3}({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln^{3}(b)ln(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*3ln^{2}(b)*0ln(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} - \frac{4a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - 15(\frac{\frac{-7}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{9}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x) - \frac{15a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{3}(a)ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*3ln^{2}(a)*0ln^{3}(b)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}(a)} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)*3ln^{2}(b)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}(b)} - \frac{15a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + 12(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)sin^{4}(x) + \frac{12a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{3}(b)ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*3ln^{2}(b)*0ln^{2}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)*2ln(a)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + 12(\frac{\frac{-5}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}})a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{4}(x) + \frac{12a^{3}b^{3}({b}^{(-4abcos(x) + 4)}((-4ab*-sin(x) + 0)ln(b) + \frac{(-4abcos(x) + 4)(0)}{(b)})){a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}({a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}((2({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{(2{b}^{(-2abcos(x) + 2)} + 4)(0)}{(a)}))ln^{3}(b)ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}*3ln^{2}(b)*0ln^{3}(a)sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(b)} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)*3ln^{2}(a)*0sin^{4}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}(a)} + \frac{12a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)*4sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + 4(\frac{\frac{-3}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}})ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x) + \frac{4ab({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})){a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{4ab{b}^{(-2abcos(x) + 2)}({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)}))ln(a)ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{4ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}*0ln(b)sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(a)} + \frac{4ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)*0sin^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}(b)} + \frac{4ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)*2sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(({a}^{({b}^{(-2abcos(x) + 2)} + 2)}((({b}^{(-2abcos(x) + 2)}((-2ab*-sin(x) + 0)ln(b) + \frac{(-2abcos(x) + 2)(0)}{(b)})) + 0)ln(a) + \frac{({b}^{(-2abcos(x) + 2)} + 2)(0)}{(a)})) + 0)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}})cos(x) - \frac{-sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\=&\frac{-90a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{120a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{2}(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{120a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(b)ln^{3}(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin(x)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{30a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin(x)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{60a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{3}(b)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{40a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{120a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{2}(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{30a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin(x)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{6ab{a}^{({b}^{(-2abcos(x) + 2)} + 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{60a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{40a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{3}(b)ln^{3}(a)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{9a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{2}(b)sin(x)cos^{2}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{60a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{3}(b)sin^{3}(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{9ab{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln(a)ln(b)sin(x)cos(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{90a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{72a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(b)ln^{2}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{144a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(b)ln^{3}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{90a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{72a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(b)ln^{4}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{56a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{4}(b)ln^{2}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{12a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{40a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{4}(b)ln^{3}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{8a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{4}(b)ln^{4}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{12a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{8a^{4}b^{4}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{4}(b)ln(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{105a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{9}{2}}} - \frac{60a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(b)ln^{3}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} - \frac{60a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{4}(b)ln^{4}(a)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{7}{2}}} + \frac{36a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{3}(a)ln^{4}(b)sin^{5}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} - \frac{18a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{20a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} - \frac{12a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(2{b}^{(-2abcos(x) + 2)} + 4)}ln^{2}(a)ln^{2}(b)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{5}{2}}} + \frac{20a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{({b}^{(-2abcos(x) + 2)} + 2)}ln^{2}(b)ln(a)sin^{3}(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{3}{2}}} + \frac{sin(x)}{({a}^{({b}^{(-2abcos(x) + 2)} + 2)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]