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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{{sin(x)}^{2}}{({a}^{(2 + {b}^{(2 - 2abcos(x))})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin^{2}(x)\right)}{dx}\\=&({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)}))sin^{2}(x) + {a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2sin(x)cos(x)\\=&-2ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{3}(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -2ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{3}(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)cos(x)\right)}{dx}\\=&-2ab({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^{3}(x) - 2ab{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^{3}(x) - \frac{2ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*0ln(b)sin^{3}(x)}{(a)} - \frac{2ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)*0sin^{3}(x)}{(b)} - 2ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)*3sin^{2}(x)cos(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)}))sin(x)cos(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}cos(x)cos(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)*-sin(x)\\=& - 10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{2}(x)cos(x) + 4a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{4}(x) - 4a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{4}(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}cos^{2}(x) - 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{2}(x)cos(x) + 4a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{4}(x) - 4a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{4}(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}cos^{2}(x) - 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin^{2}(x)\right)}{dx}\\=& - 10ab({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)cos(x) - 10ab{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)cos(x) - \frac{10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*0ln(b)sin^{2}(x)cos(x)}{(a)} - \frac{10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)*0sin^{2}(x)cos(x)}{(b)} - 10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)*2sin(x)cos(x)cos(x) - 10ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{2}(x)*-sin(x) + 4a^{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^{4}(x) + 4a^{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^{4}(x) + \frac{4a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2ln(b)*0ln^{2}(a)sin^{4}(x)}{(b)} + \frac{4a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)*2ln(a)*0sin^{4}(x)}{(a)} + 4a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)*4sin^{3}(x)cos(x) - 4a^{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^{4}(x) - 4a^{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^{4}(x) - \frac{4a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2ln(b)*0ln(a)sin^{4}(x)}{(b)} - \frac{4a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)*0sin^{4}(x)}{(a)} - 4a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)*4sin^{3}(x)cos(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)}))cos^{2}(x) + 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*-2cos(x)sin(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)}))sin^{2}(x) - 2{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2sin(x)cos(x)\\=& - 36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{3}(x)cos(x) + 36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)cos(x) - 24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin(x)cos^{2}(x) + 24a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{2}(a)sin^{5}(x) - 8a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{3}(a)sin^{5}(x) - 8a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln(a)sin^{5}(x) + 14ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{3}(x) - 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{3}(x)cos(x) + 36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)cos(x) - 24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin(x)cos^{2}(x) + 24a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{2}(a)sin^{5}(x) - 8a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{3}(a)sin^{5}(x) - 8a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln(a)sin^{5}(x) + 14ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{3}(x) - 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)cos(x)\right)}{dx}\\=& - 36a^{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)cos(x) - 36a^{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)cos(x) - \frac{36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2ln(b)*0ln(a)sin^{3}(x)cos(x)}{(b)} - \frac{36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)*0sin^{3}(x)cos(x)}{(a)} - 36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)*3sin^{2}(x)cos(x)cos(x) - 36a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{3}(x)*-sin(x) + 36a^{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)cos(x) + 36a^{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)cos(x) + \frac{36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*2ln(b)*0ln^{2}(a)sin^{3}(x)cos(x)}{(b)} + \frac{36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)*2ln(a)*0sin^{3}(x)cos(x)}{(a)} + 36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)*3sin^{2}(x)cos(x)cos(x) + 36a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{3}(x)*-sin(x) - 24ab({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^{2}(x) - 24ab{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^{2}(x) - \frac{24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*0ln(b)sin(x)cos^{2}(x)}{(a)} - \frac{24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)*0sin(x)cos^{2}(x)}{(b)} - 24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)cos(x)cos^{2}(x) - 24ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin(x)*-2cos(x)sin(x) + 24a^{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^{5}(x) + 24a^{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^{5}(x) + \frac{24a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*3ln^{2}(b)*0ln^{2}(a)sin^{5}(x)}{(b)} + \frac{24a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)*2ln(a)*0sin^{5}(x)}{(a)} + 24a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{2}(a)*5sin^{4}(x)cos(x) - 8a^{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^{5}(x) - 8a^{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^{5}(x) - \frac{8a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*3ln^{2}(b)*0ln^{3}(a)sin^{5}(x)}{(b)} - \frac{8a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)*3ln^{2}(a)*0sin^{5}(x)}{(a)} - 8a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{3}(a)*5sin^{4}(x)cos(x) - 8a^{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^{5}(x) - 8a^{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^{5}(x) - \frac{8a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*3ln^{2}(b)*0ln(a)sin^{5}(x)}{(b)} - \frac{8a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)*0sin^{5}(x)}{(a)} - 8a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln(a)*5sin^{4}(x)cos(x) + 14ab({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^{3}(x) + 14ab{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^{3}(x) + \frac{14ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}*0ln(b)sin^{3}(x)}{(a)} + \frac{14ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)*0sin^{3}(x)}{(b)} + 14ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)*3sin^{2}(x)cos(x) - 8({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)}))sin(x)cos(x) - 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}cos(x)cos(x) - 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin(x)*-sin(x)\\=& - 112a^{3}b^{3}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln(a)sin^{4}(x)cos(x) + 336a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{2}(a)sin^{4}(x)cos(x) - 156a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{2}(x)cos^{2}(x) + 106ab{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln(a)ln(b)sin^{2}(x)cos(x) - 112a^{3}b^{3}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{3}(b)ln^{3}(a)sin^{4}(x)cos(x) + 156a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{2}(x)cos^{2}(x) - 24ab{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}{b}^{(-2abcos(x) + 2)}ln(b)ln(a)cos^{3}(x) + 112a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{4}(b)ln^{2}(a)sin^{6}(x) - 80a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{4}(b)ln^{3}(a)sin^{6}(x) + 16a^{4}b^{4}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{4}(b)ln^{4}(a)sin^{6}(x) + 64a^{2}b^{2}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln(a)sin^{4}(x) - 16a^{4}b^{4}{b}^{(-2abcos(x) + 2)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{4}(b)ln(a)sin^{6}(x) - 64a^{2}b^{2}{b}^{(-4abcos(x) + 4)}{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}ln^{2}(b)ln^{2}(a)sin^{4}(x) - 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}cos^{2}(x) + 8{a}^{(-{b}^{(-2abcos(x) + 2)} - 2)}sin^{2}(x)\\ \end{split}\end{equation} \]