求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
本次共计算 1 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{{sin(x)}^{cos(x)}}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {{sin(x)}^{cos(x)}}^{x}\right)}{dx}\\=&({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))\\=&{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( {{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)}\right)}{dx}\\=&({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + \frac{x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{x{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)}\\=& - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}cos(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}cos(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)}\right)}{dx}\\=& - 2({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) - \frac{2{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + \frac{2{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} + \frac{2({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)} + ({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin^{2}(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))*2sin(x)cos(x) - 2*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 2x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{2}(x) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{2}(x)}{(sin(x))} - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-2cos(x)sin(x) - 3{{sin(x)}^{cos(x)}}^{x}cos(x) - 3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos(x) - 3x{{sin(x)}^{cos(x)}}^{x}*-sin(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)cos(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{2}(x)} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - \frac{{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)}\\=& - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 9{{sin(x)}^{cos(x)}}^{x}cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + 3x{{sin(x)}^{cos(x)}}^{x}sin(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 9{{sin(x)}^{cos(x)}}^{x}cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + 3x{{sin(x)}^{cos(x)}}^{x}sin(x)\right)}{dx}\\=& - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{3*2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{4}(x)}{({sin(x)}^{cos(x)})sin^{2}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - 12{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 12x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{2}(x) - \frac{12x{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{2}(x)}{(sin(x))} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-2cos(x)sin(x) - 9({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos(x) - 9{{sin(x)}^{cos(x)}}^{x}*-sin(x) - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}cos(x)cos(x)}{(sin(x))} - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-sin(x) - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - 2{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - 2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{2x{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 2*2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + 2x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)ln({sin(x)}^{cos(x)})sin^{2}(x)}{(sin(x))} + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin^{2}(x)}{({sin(x)}^{cos(x)})} + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})*2sin(x)cos(x) - 3*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})cos^{2}(x)}{(sin(x))} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})*-2cos(x)sin(x) - 9{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) - 9x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos(x) - \frac{9x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos(x)}{({sin(x)}^{cos(x)})} - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-sin(x) + \frac{3{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} - 2{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) - 2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) - \frac{2x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))cos(x)}{({sin(x)}^{cos(x)})} - \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)cos(x)}{(sin(x))} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))*-sin(x) + \frac{6({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} + 3*3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 3x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin(x)cos^{2}(x)}{(sin(x))} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos(x)cos^{2}(x) + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)*-2cos(x)sin(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{6x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{2}(x)} + \frac{6x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{6x{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{3}(x)}{({sin(x)}^{cos(x)})sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-3cos^{2}(x)sin(x)}{sin^{2}(x)} - \frac{3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)} + ({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{3}({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}*3ln^{2}({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln^{2}({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos(x) - \frac{3*3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{4}(x)}{(sin(x))sin(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-cos(x)cos^{4}(x)}{sin^{2}(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-4cos^{3}(x)sin(x)}{sin(x)} - 3*2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))cos^{2}(x)}{({sin(x)}^{cos(x)})} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)cos^{2}(x)}{(sin(x))} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))*-2cos(x)sin(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})cos(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})*-sin(x) + 9*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + 9x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x)cos(x) + \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)cos(x)}{(sin(x))} + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x)cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)*-sin(x) + 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln^{2}(sin(x))sin^{2}(x)}{({sin(x)}^{cos(x)})} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))*2sin(x)cos(x) + 3*2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin(x)cos(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin(x)cos(x)}{(sin(x))} + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos(x)cos(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)*-sin(x) + 6{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + 6x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))*2sin(x)cos(x) - \frac{9*2x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{9x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin(x)} - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{3}(x)}{sin^{2}(x)} - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin(x)} - \frac{3*2x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - \frac{3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{5}(x)}{sin^{3}(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{5}(x)}{sin^{4}(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*-5cos^{4}(x)sin(x)}{sin^{3}(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) - x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{3}(sin(x))sin^{3}(x) - \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*3ln^{2}(sin(x))cos(x)sin^{3}(x)}{(sin(x))} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))*3sin^{2}(x)cos(x) + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{6}(x)}{sin^{3}(x)} + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{6}(x)}{sin^{4}(x)} + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*-6cos^{5}(x)sin(x)}{sin^{3}(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{4}(x)}{sin^{4}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{3}(x)} + 3{{sin(x)}^{cos(x)}}^{x}sin(x) + 3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))sin(x) + 3x{{sin(x)}^{cos(x)}}^{x}cos(x)\\=& - 8{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin(x)} - 27x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) + \frac{12{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 24{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 36{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) - 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + \frac{24x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{6x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + 8x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos^{2}(x) + \frac{4x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{6}(x)}{sin^{3}(x)} + \frac{12x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} - \frac{12x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{5}(x)}{sin^{3}(x)} - \frac{36x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin(x)} - \frac{36x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{72x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{6x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} + \frac{8{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} - 8{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 24x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 72x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + \frac{8{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} - \frac{12{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - 21x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) + 21x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos(x) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{3}(x)}{sin(x)} - 8x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{4}(x)}{sin(x)} - 18x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos(x) + 7x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos(x) + 15x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x)cos(x) + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin(x)} + 5x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin(x)cos(x) + 36x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 4x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{3}(x)} + \frac{4x{{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 4x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos^{2}(x) - 18x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x)cos(x) - 4x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos(x) - 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))ln({sin(x)}^{cos(x)})sin^{3}(x) + 16x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + \frac{8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 4x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{2}(x)cos^{2}(x) + \frac{12{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 6x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{4}(x) + 36x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{3}(x) + 6x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{3}(x) + \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{5}(x)}{sin^{2}(x)} - \frac{4x^{4}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{6}(x)}{sin^{2}(x)} - \frac{24x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} + 12{{sin(x)}^{cos(x)}}^{x}sin(x) - 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{3}({sin(x)}^{cos(x)})sin(x) + 12{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{18x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{2}(x)} + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln^{2}({sin(x)}^{cos(x)})sin^{2}(x) + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 6x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{2}(x)cos(x) + 39x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{2}(x) + 14x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) + 8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{2}(x) + {{sin(x)}^{cos(x)}}^{x}ln^{4}({sin(x)}^{cos(x)}) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin^{2}(x)} - 4x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + \frac{26x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - 12x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{7}(x)}{sin^{4}(x)} + \frac{11x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{4}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{3}(sin(x))sin^{3}(x) + x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{4}(sin(x))sin^{4}(x) + 12x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})sin(x) - \frac{10x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 12x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin^{2}(x) + \frac{x^{4}{{sin(x)}^{cos(x)}}^{x}cos^{8}(x)}{sin^{4}(x)} - \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{4}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{{sin(x)}^{cos(x)}}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {{sin(x)}^{cos(x)}}^{x}\right)}{dx}\\=&({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))\\=&{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( {{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)}\right)}{dx}\\=&({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + \frac{x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{x{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)}\\=& - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}cos(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}cos(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)}\right)}{dx}\\=& - 2({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) - \frac{2{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} - 2{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + \frac{2{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} + \frac{2({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)} + ({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin^{2}(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))*2sin(x)cos(x) - 2*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 2x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{2}(x) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{2}(x)}{(sin(x))} - 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-2cos(x)sin(x) - 3{{sin(x)}^{cos(x)}}^{x}cos(x) - 3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos(x) - 3x{{sin(x)}^{cos(x)}}^{x}*-sin(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)cos(x)}{(sin(x))} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-sin(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{2}(x)} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - \frac{{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} - \frac{x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin^{2}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{x{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)}\\=& - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 9{{sin(x)}^{cos(x)}}^{x}cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + 3x{{sin(x)}^{cos(x)}}^{x}sin(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 9{{sin(x)}^{cos(x)}}^{x}cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + {{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)}) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + 3x{{sin(x)}^{cos(x)}}^{x}sin(x)\right)}{dx}\\=& - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - 3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + \frac{3*2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{4}(x)}{({sin(x)}^{cos(x)})sin^{2}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - 12{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 12x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{2}(x) - \frac{12x{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{2}(x)}{(sin(x))} - 12x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-2cos(x)sin(x) - 9({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos(x) - 9{{sin(x)}^{cos(x)}}^{x}*-sin(x) - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}cos(x)cos(x)}{(sin(x))} - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-sin(x) - 3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - \frac{3{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - 3{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - 2{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - 2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{2x{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x)}{({sin(x)}^{cos(x)})} - \frac{2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos(x)sin(x)}{(sin(x))} - 2x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 2*2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + 2x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)ln({sin(x)}^{cos(x)})sin^{2}(x)}{(sin(x))} + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin^{2}(x)}{({sin(x)}^{cos(x)})} + 2x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})*2sin(x)cos(x) - 3*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})cos^{2}(x)}{(sin(x))} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})*-2cos(x)sin(x) - 9{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) - 9x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos(x) - \frac{9x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos(x)}{({sin(x)}^{cos(x)})} - 9x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-sin(x) + \frac{3{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{3x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} - 2{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) - 2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) - \frac{2x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))cos(x)}{({sin(x)}^{cos(x)})} - \frac{2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)cos(x)}{(sin(x))} - 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))*-sin(x) + \frac{6({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{({sin(x)}^{cos(x)})sin(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{6{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)sin(x)}{sin(x)} + 3*3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 3x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin(x)cos^{2}(x)}{(sin(x))} + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos(x)cos^{2}(x) + 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)*-2cos(x)sin(x) + \frac{6{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + \frac{6x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{2}(x)} + \frac{6x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{4}(x)}{sin^{3}(x)} + \frac{6x{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{3}(x)}{({sin(x)}^{cos(x)})sin^{2}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*-3cos^{2}(x)sin(x)}{sin^{2}(x)} - \frac{3({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin^{2}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}*-2cos(x)cos^{3}(x)}{sin^{3}(x)} - \frac{3{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin^{2}(x)} + ({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{3}({sin(x)}^{cos(x)}) + \frac{{{sin(x)}^{cos(x)}}^{x}*3ln^{2}({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))}{({sin(x)}^{cos(x)})} - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln^{2}({sin(x)}^{cos(x)})sin(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*2ln({sin(x)}^{cos(x)})({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))sin(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos(x) - \frac{3*3x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}cos(x)cos^{4}(x)}{(sin(x))sin(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-cos(x)cos^{4}(x)}{sin^{2}(x)} - \frac{3x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))*-4cos^{3}(x)sin(x)}{sin(x)} - 3*2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))cos^{2}(x)}{({sin(x)}^{cos(x)})} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x)cos^{2}(x)}{(sin(x))} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))*-2cos(x)sin(x) - {{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) - \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)ln({sin(x)}^{cos(x)})cos(x)}{(sin(x))} - \frac{x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos(x)}{({sin(x)}^{cos(x)})} - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})*-sin(x) + 9*2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + 9x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x)cos(x) + \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)cos(x)}{(sin(x))} + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x)cos(x) + 9x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)*-sin(x) + 2x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln^{2}(sin(x))sin^{2}(x)}{({sin(x)}^{cos(x)})} + \frac{x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))*2sin(x)cos(x) + 3*2x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin(x)cos(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin(x)cos(x)}{(sin(x))} + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos(x)cos(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)*-sin(x) + 6{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + 6x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{2}(sin(x))sin^{2}(x) + \frac{6x{{sin(x)}^{cos(x)}}^{x}*2ln(sin(x))cos(x)sin^{2}(x)}{(sin(x))} + 6x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))*2sin(x)cos(x) - \frac{9*2x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{9x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{3}(x)}{sin(x)} - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{3}(x)}{sin^{2}(x)} - \frac{9x^{2}{{sin(x)}^{cos(x)}}^{x}*-3cos^{2}(x)sin(x)}{sin(x)} - \frac{3*2x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} - \frac{3x^{2}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{5}(x)}{sin^{3}(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{5}(x)}{sin^{4}(x)} - \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}*-5cos^{4}(x)sin(x)}{sin^{3}(x)} - 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) - x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln^{3}(sin(x))sin^{3}(x) - \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*3ln^{2}(sin(x))cos(x)sin^{3}(x)}{(sin(x))} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))*3sin^{2}(x)cos(x) + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{2}(x)}{sin(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-2cos(x)sin(x)}{sin(x)} + {{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))ln(sin(x))sin(x) + \frac{x{{sin(x)}^{cos(x)}}^{x}cos(x)sin(x)}{(sin(x))} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) + \frac{3x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} + \frac{x^{3}({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{6}(x)}{sin^{3}(x)} + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{6}(x)}{sin^{4}(x)} + \frac{x^{3}{{sin(x)}^{cos(x)}}^{x}*-6cos^{5}(x)sin(x)}{sin^{3}(x)} + \frac{2{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} + \frac{2x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))cos^{4}(x)}{sin^{3}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-3cos(x)cos^{4}(x)}{sin^{4}(x)} + \frac{2x{{sin(x)}^{cos(x)}}^{x}*-4cos^{3}(x)sin(x)}{sin^{3}(x)} + 3{{sin(x)}^{cos(x)}}^{x}sin(x) + 3x({{sin(x)}^{cos(x)}}^{x}((1)ln({sin(x)}^{cos(x)}) + \frac{(x)(({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))})))}{({sin(x)}^{cos(x)})}))sin(x) + 3x{{sin(x)}^{cos(x)}}^{x}cos(x)\\=& - 8{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin(x)} - 27x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) + \frac{12{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 24{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) - 36{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos(x) - 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos(x) + \frac{24x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + \frac{6x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{2}(x)} + 8x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos^{2}(x) + \frac{4x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{6}(x)}{sin^{3}(x)} + \frac{12x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{3}(x)} - \frac{12x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{5}(x)}{sin^{3}(x)} - \frac{36x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin(x)} - \frac{36x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin(x)} - \frac{72x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin(x)} - \frac{6x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} + \frac{8{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{3}(x)} - 8{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos(x) + 24x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos(x) + 72x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x)cos(x) + \frac{8{{sin(x)}^{cos(x)}}^{x}cos^{2}(x)}{sin(x)} - \frac{12{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin^{2}(x)} - 21x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{2}(x) + 21x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos(x) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{3}(x)}{sin(x)} - 8x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos^{2}(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))cos^{4}(x)}{sin(x)} - 18x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})cos(x) - 2x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos(x) + 7x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin(x)cos(x) + 15x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x)cos(x) + \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})cos^{3}(x)}{sin(x)} + 5x^{2}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin(x)cos(x) + 36x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin(x)cos^{2}(x) + 4x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin(x)cos^{2}(x) + \frac{8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{4}(x)}{sin^{3}(x)} + \frac{4x{{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 4x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})cos^{2}(x) - 18x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x)cos(x) - 4x{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln(sin(x))cos(x) - 3x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))ln({sin(x)}^{cos(x)})sin^{3}(x) + 16x{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln({sin(x)}^{cos(x)})sin^{2}(x) + \frac{8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})cos^{2}(x)}{sin(x)} - 4x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{2}(x)cos^{2}(x) + \frac{12{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} + 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 6x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{4}(x) + 36x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{3}(x) + 6x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{3}(x) + \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{5}(x)}{sin^{2}(x)} - \frac{4x^{4}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{6}(x)}{sin^{2}(x)} - \frac{24x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{3}(x)} + 12{{sin(x)}^{cos(x)}}^{x}sin(x) - 4{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{2}({sin(x)}^{cos(x)})sin(x) - x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln^{3}({sin(x)}^{cos(x)})sin(x) + 12{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) - 3x{{sin(x)}^{cos(x)}}^{x}ln^{3}({sin(x)}^{cos(x)})ln(sin(x))sin(x) - \frac{18x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{2}(x)} + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))ln^{2}({sin(x)}^{cos(x)})sin^{2}(x) + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))ln({sin(x)}^{cos(x)})sin(x) - 6x^{3}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{2}(x)cos(x) + 39x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{2}(x) + 14x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{2}(x) + 8x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{2}(sin(x))sin^{2}(x) + 3x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln(sin(x))sin(x) + 3x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))cos^{2}(x) + {{sin(x)}^{cos(x)}}^{x}ln^{4}({sin(x)}^{cos(x)}) - \frac{2x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos^{4}(x)}{sin^{2}(x)} - 4x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{2}(sin(x))sin^{2}(x) + \frac{26x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{4}(x)}{sin^{2}(x)} - 12x^{2}{{sin(x)}^{cos(x)}}^{x}ln^{3}(sin(x))sin^{3}(x) - \frac{6x^{3}{{sin(x)}^{cos(x)}}^{x}cos^{7}(x)}{sin^{4}(x)} + \frac{11x^{2}{{sin(x)}^{cos(x)}}^{x}cos^{6}(x)}{sin^{4}(x)} - x^{3}{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})ln^{3}(sin(x))sin^{3}(x) + x^{4}{{sin(x)}^{cos(x)}}^{x}ln^{4}(sin(x))sin^{4}(x) + 12x{{sin(x)}^{cos(x)}}^{x}ln({sin(x)}^{cos(x)})sin(x) - \frac{10x{{sin(x)}^{cos(x)}}^{x}cos^{3}(x)}{sin^{2}(x)} + x{{sin(x)}^{cos(x)}}^{x}ln(sin(x))cos(x) - 12x^{2}{{sin(x)}^{cos(x)}}^{x}ln(sin(x))sin^{2}(x) + \frac{x^{4}{{sin(x)}^{cos(x)}}^{x}cos^{8}(x)}{sin^{4}(x)} - \frac{6x{{sin(x)}^{cos(x)}}^{x}cos^{5}(x)}{sin^{4}(x)}\\ \end{split}\end{equation} \]
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