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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{1}{tan(xsin(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{tan(xsin(x))}\right)}{dx}\\=&\frac{-sec^{2}(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))}\\=&\frac{-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))}\right)}{dx}\\=&\frac{-cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{sin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{sin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{x*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{xcos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))}\\=&\frac{-2cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))}\right)}{dx}\\=&\frac{-2*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2cos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{2*2sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2sin^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{2sin^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{4sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xcos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{4xsin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{2*2sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2sin^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2sin^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{4sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xcos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{4xsin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} + \frac{sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xsin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{xsin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{2*2xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2x^{2}*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2x^{2}cos^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{2x^{2}cos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{2*2xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2x^{2}*-2cos(x)sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2x^{2}cos^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2x^{2}cos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))}\\=&\frac{3sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{12sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{12sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6sin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10sin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6xsin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4sin^{3}(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)sec^{2}(xsin(x)) + \frac{6xsin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 12x^{2}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6x^{3}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10x^{3}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4x^{3}cos^{3}(x)sec^{2}(xsin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{12sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{12sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6sin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10sin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6xsin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4sin^{3}(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)sec^{2}(xsin(x)) + \frac{6xsin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 12x^{2}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6x^{3}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10x^{3}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4x^{3}cos^{3}(x)sec^{2}(xsin(x))\right)}{dx}\\=&\frac{3cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{3sin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{3sin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{12cos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12sin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12sin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{12sin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{12cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12x*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{12xcos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{12cos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12sin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12sin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{12sin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{12cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12x*-2cos(x)sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{12xcos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{6*3sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6sin^{3}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{6sin^{3}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} - \frac{18sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x*2sin(x)cos(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)*-sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{10*3sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10sin^{3}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{10sin^{3}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{30sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x*2sin(x)cos(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)*-sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{6sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x*2sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6xsin^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6xsin^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{18*2xsin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}cos(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}sin(x)*-2cos(x)sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{30*2xsin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}cos(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}sin(x)*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - 4*3sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 4sin^{3}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) - 12sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 12x*2sin(x)cos(x)cos(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)*-sin(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) + \frac{6sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x*2sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6xsin^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{6xsin^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - 12*2xsin(x)cos^{2}(x)sec^{2}(xsin(x)) - 12x^{2}cos(x)cos^{2}(x)sec^{2}(xsin(x)) - 12x^{2}sin(x)*-2cos(x)sin(x)sec^{2}(xsin(x)) - 12x^{2}sin(x)cos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) + \frac{cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{x*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xcos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{xcos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{6*2xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}cos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{6*2xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}cos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{6*3x^{2}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{3}*-3cos^{2}(x)sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{3}cos^{3}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{6x^{3}cos^{3}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{10*3x^{2}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10x^{3}*-3cos^{2}(x)sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10x^{3}cos^{3}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{10x^{3}cos^{3}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - 4*3x^{2}cos^{3}(x)sec^{2}(xsin(x)) - 4x^{3}*-3cos^{2}(x)sin(x)sec^{2}(xsin(x)) - 4x^{3}cos^{3}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))\\=&\frac{4cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{24sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{56xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{24sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{56xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{24cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{24sin^{4}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{72sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{144xsin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{120sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{240xsin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{72x^{2}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{120x^{2}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{24cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{56sin^{4}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} - 48sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 96xsin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{96x^{3}sin(x)cos^{3}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - 48x^{2}cos^{3}(x)sec^{2}(xsin(x)) + \frac{96xsin^{3}(x)cos(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{224xsin^{3}(x)cos(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{36xsin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{144x^{2}sin^{2}(x)cos^{2}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{336x^{2}sin^{2}(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{40sin^{4}(x)sec^{4}(xsin(x))}{tan(xsin(x))} + \frac{160xsin^{3}(x)cos(x)sec^{4}(xsin(x))}{tan(xsin(x))} - \frac{60xsin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{240x^{2}sin^{2}(x)cos^{2}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - \frac{224x^{3}sin(x)cos^{3}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{72x^{2}sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{120x^{2}sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{160x^{3}sin(x)cos^{3}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - 8sin^{4}(x)tan(xsin(x))sec^{2}(xsin(x)) - 32xsin^{3}(x)cos(x)tan(xsin(x))sec^{2}(xsin(x)) + 24xsin^{3}(x)sec^{2}(xsin(x)) + \frac{36x^{3}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + 48x^{2}sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 48x^{2}sin^{2}(x)cos^{2}(x)tan(xsin(x))sec^{2}(xsin(x)) - \frac{60x^{3}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{8x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{8x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 32x^{3}sin(x)cos^{3}(x)tan(xsin(x))sec^{2}(xsin(x)) + 24x^{3}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{24x^{4}cos^{4}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{56x^{4}cos^{4}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{40x^{4}cos^{4}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - 8x^{4}cos^{4}(x)tan(xsin(x))sec^{2}(xsin(x))\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{1}{tan(xsin(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{tan(xsin(x))}\right)}{dx}\\=&\frac{-sec^{2}(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))}\\=&\frac{-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))}\right)}{dx}\\=&\frac{-cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{sin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{sin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{x*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xcos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{xcos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))}\\=&\frac{-2cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{2x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))}\right)}{dx}\\=&\frac{-2*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2cos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} - \frac{2cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{2*2sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2sin^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{2sin^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{4sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xcos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{4xsin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{4xsin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{2*2sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2sin^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2sin^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{4sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xcos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{4xsin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{4xsin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} + \frac{sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xsin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{xsin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{2*2xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2x^{2}*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{2x^{2}cos^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{2x^{2}cos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{2*2xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2x^{2}*-2cos(x)sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{2x^{2}cos^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{2x^{2}cos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))}\\=&\frac{3sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{12sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{12sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6sin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10sin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6xsin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4sin^{3}(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)sec^{2}(xsin(x)) + \frac{6xsin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 12x^{2}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6x^{3}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10x^{3}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4x^{3}cos^{3}(x)sec^{2}(xsin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{12sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{12sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6sin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10sin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6xsin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4sin^{3}(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)sec^{2}(xsin(x)) + \frac{6xsin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 12x^{2}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{xcos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{6x^{3}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{10x^{3}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - 4x^{3}cos^{3}(x)sec^{2}(xsin(x))\right)}{dx}\\=&\frac{3cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{3sin(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{3sin(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{12cos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12sin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12sin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{12sin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{12cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12x*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{12xcos^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} + \frac{12xcos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{12cos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12sin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12sin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{12sin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{12cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12x*-2cos(x)sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{12xcos^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{12xcos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{6*3sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6sin^{3}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{6sin^{3}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} - \frac{18sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x*2sin(x)cos(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)*-sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{18xsin^{2}(x)cos(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{10*3sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10sin^{3}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{10sin^{3}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} + \frac{30sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x*2sin(x)cos(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)*-sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{30xsin^{2}(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{6sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x*2sin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6xsin^{2}(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6xsin^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} - \frac{18*2xsin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}cos(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}sin(x)*-2cos(x)sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{18x^{2}sin(x)cos^{2}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{30*2xsin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}cos(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}sin(x)*-2cos(x)sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{30x^{2}sin(x)cos^{2}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - 4*3sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 4sin^{3}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) - 12sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 12x*2sin(x)cos(x)cos(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)*-sin(x)sec^{2}(xsin(x)) - 12xsin^{2}(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) + \frac{6sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x*2sin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6xsin^{2}(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{6xsin^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - 12*2xsin(x)cos^{2}(x)sec^{2}(xsin(x)) - 12x^{2}cos(x)cos^{2}(x)sec^{2}(xsin(x)) - 12x^{2}sin(x)*-2cos(x)sin(x)sec^{2}(xsin(x)) - 12x^{2}sin(x)cos^{2}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x)) + \frac{cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{x*-sin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{xcos(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{3}(xsin(x))} + \frac{xcos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - \frac{6*2xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}cos(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin(x)*-sin(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)*-3sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{2}sin(x)cos(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{3}(xsin(x))} + \frac{6*2xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}cos(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin(x)*-sin(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin(x)cos(x)*-sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{2}(xsin(x))}{tan^{2}(xsin(x))} + \frac{6x^{2}sin(x)cos(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan(xsin(x))} - \frac{6*3x^{2}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{3}*-3cos^{2}(x)sin(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{6x^{3}cos^{3}(x)*-4sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{6}(xsin(x))}{tan^{5}(xsin(x))} - \frac{6x^{3}cos^{3}(x)*6sec^{6}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{4}(xsin(x))} + \frac{10*3x^{2}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10x^{3}*-3cos^{2}(x)sin(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{10x^{3}cos^{3}(x)*-2sec^{2}(xsin(x))(sin(x) + xcos(x))sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{10x^{3}cos^{3}(x)*4sec^{4}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))}{tan^{2}(xsin(x))} - 4*3x^{2}cos^{3}(x)sec^{2}(xsin(x)) - 4x^{3}*-3cos^{2}(x)sin(x)sec^{2}(xsin(x)) - 4x^{3}cos^{3}(x)*2sec^{2}(xsin(x))tan(xsin(x))(sin(x) + xcos(x))\\=&\frac{4cos(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{24sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{56xsin(x)cos(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{24sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{56xsin(x)cos(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{24cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{24sin^{4}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{72sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{144xsin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{120sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{240xsin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{72x^{2}cos^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{120x^{2}cos^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{24cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - \frac{56sin^{4}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} - 48sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 96xsin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{96x^{3}sin(x)cos^{3}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - 48x^{2}cos^{3}(x)sec^{2}(xsin(x)) + \frac{96xsin^{3}(x)cos(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{224xsin^{3}(x)cos(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{36xsin^{3}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + \frac{144x^{2}sin^{2}(x)cos^{2}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{336x^{2}sin^{2}(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{40sin^{4}(x)sec^{4}(xsin(x))}{tan(xsin(x))} + \frac{160xsin^{3}(x)cos(x)sec^{4}(xsin(x))}{tan(xsin(x))} - \frac{60xsin^{3}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{240x^{2}sin^{2}(x)cos^{2}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - \frac{224x^{3}sin(x)cos^{3}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{72x^{2}sin^{2}(x)cos(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} - \frac{120x^{2}sin^{2}(x)cos(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} + \frac{160x^{3}sin(x)cos^{3}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - 8sin^{4}(x)tan(xsin(x))sec^{2}(xsin(x)) - 32xsin^{3}(x)cos(x)tan(xsin(x))sec^{2}(xsin(x)) + 24xsin^{3}(x)sec^{2}(xsin(x)) + \frac{36x^{3}sin(x)cos^{2}(x)sec^{6}(xsin(x))}{tan^{4}(xsin(x))} + 48x^{2}sin^{2}(x)cos(x)sec^{2}(xsin(x)) - 48x^{2}sin^{2}(x)cos^{2}(x)tan(xsin(x))sec^{2}(xsin(x)) - \frac{60x^{3}sin(x)cos^{2}(x)sec^{4}(xsin(x))}{tan^{2}(xsin(x))} - \frac{xsin(x)sec^{2}(xsin(x))}{tan^{2}(xsin(x))} - \frac{8x^{2}cos^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} + \frac{8x^{2}cos^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} + \frac{6x^{2}sin^{2}(x)sec^{4}(xsin(x))}{tan^{3}(xsin(x))} - \frac{6x^{2}sin^{2}(x)sec^{2}(xsin(x))}{tan(xsin(x))} - 32x^{3}sin(x)cos^{3}(x)tan(xsin(x))sec^{2}(xsin(x)) + 24x^{3}sin(x)cos^{2}(x)sec^{2}(xsin(x)) + \frac{24x^{4}cos^{4}(x)sec^{8}(xsin(x))}{tan^{5}(xsin(x))} - \frac{56x^{4}cos^{4}(x)sec^{6}(xsin(x))}{tan^{3}(xsin(x))} + \frac{40x^{4}cos^{4}(x)sec^{4}(xsin(x))}{tan(xsin(x))} - 8x^{4}cos^{4}(x)tan(xsin(x))sec^{2}(xsin(x))\\ \end{split}\end{equation} \]
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