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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sin(xsin(\frac{1}{x})))}{(xsin(\frac{1}{x}))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sin(xsin(\frac{1}{x}))}{xsin(\frac{1}{x})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{sin(xsin(\frac{1}{x}))}{xsin(\frac{1}{x})}\right)}{dx}\\=&\frac{-sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{xsin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{xsin^{2}(\frac{1}{x})x^{2}}\\=&\frac{cos(xsin(\frac{1}{x}))}{x} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cos(xsin(\frac{1}{x}))}{x} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})}\right)}{dx}\\=&\frac{-cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x} + \frac{-3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{3}(\frac{1}{x})x^{2}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}sin^{2}(\frac{1}{x})x^{2}} - \frac{-2cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin^{2}(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}sin(\frac{1}{x})x^{2}} - \frac{-2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{2}sin^{2}(\frac{1}{x})x^{2}}\\=&\frac{-2cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} - \frac{sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x} + \frac{sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} - \frac{sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x} + \frac{sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})}\right)}{dx}\\=&\frac{-2*-2cos(xsin(\frac{1}{x}))}{x^{3}} - \frac{2*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{2}} + \frac{4*-3cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{4*-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})x^{2}} + \frac{4*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} + \frac{4cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}sin(\frac{1}{x})x^{2}} - \frac{2*-4cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2*-2cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{3}(\frac{1}{x})x^{2}} - \frac{2*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})x^{2}} - \frac{2cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2*-5sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2*-3cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{4}(\frac{1}{x})x^{2}} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{4*-4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4*-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{3}(\frac{1}{x})x^{2}} - \frac{4cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{2*-2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}} + \frac{2sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}x^{2}} - \frac{-3sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})x^{2}} - \frac{sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{3}sin(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x} - \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{xx^{2}} + \frac{-5sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}sin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{-4cos(xsin(\frac{1}{x}))}{x^{5}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}} + \frac{2*-3sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}sin(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{3}sin^{2}(\frac{1}{x})x^{2}}\\=& - \frac{cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}} - \frac{18cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{16cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} + \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{18sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{9cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} - \frac{9sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{3sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x} - \frac{9sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{4}} - \frac{6sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{4}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - \frac{cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}} - \frac{18cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{16cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} + \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{18sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{9cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} - \frac{9sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{3sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x} - \frac{9sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{4}} - \frac{6sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{4}}\right)}{dx}\\=& - \frac{-3cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{3}} - \frac{cos(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{3}x^{2}} - \frac{18*-4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} - \frac{18*-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} - \frac{18*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{18cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} + \frac{16*-5cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{16*-2cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{16*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{16cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4*-6cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{4*-cos(\frac{1}{x})*-cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})x^{2}} - \frac{4*-sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})x^{2}} - \frac{4cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin(\frac{1}{x})} + \frac{9*-4sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{9sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} - \frac{6*-6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin^{3}(\frac{1}{x})} - \frac{6*-3cos(\frac{1}{x})*-cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{4}(\frac{1}{x})x^{2}} - \frac{6*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})x^{2}} - \frac{6cos^{3}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2*-5cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2*-2cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{2*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{6*-7sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{8}sin^{4}(\frac{1}{x})} + \frac{6*-4cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{5}(\frac{1}{x})x^{2}} + \frac{6cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{7}sin^{4}(\frac{1}{x})x^{2}} - \frac{2*-5sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})*-cos^{3}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{2sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{18*-6sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{18*-3cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{4}(\frac{1}{x})x^{2}} - \frac{18cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{6}sin^{3}(\frac{1}{x})x^{2}} + \frac{3*-2sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{3cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}x^{2}} + \frac{3sin(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}x^{2}} + \frac{4*-7sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{4cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} + \frac{4sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})*-cos(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})x^{2}} + \frac{4sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{7}sin^{2}(\frac{1}{x})x^{2}} - \frac{-5sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{2*-3cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{2*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{3}x^{2}} - \frac{2cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}} + \frac{18*-5sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{18*-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{18cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{18sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{-4cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} - \frac{-6cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{6}sin(\frac{1}{x})x^{2}} + \frac{6*-3cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{6*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}} + \frac{9*-5cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{9*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}} + \frac{-7sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})x^{2}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{7}sin^{2}(\frac{1}{x})x^{2}} - \frac{3*-5sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}} - \frac{3cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{5}} - \frac{3sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{5}x^{2}} - \frac{9*-6sin(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin(\frac{1}{x})} - \frac{9sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{6}sin^{2}(\frac{1}{x})x^{2}} + \frac{3*-2sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{3}} + \frac{3cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x^{2}} + \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{x^{2}x^{2}} - \frac{-sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{2}} - \frac{2sin(\frac{1}{x})cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{xx^{2}} - \frac{sin^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x} - \frac{9*-3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}} - \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}} - \frac{9sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}x^{2}} + \frac{-4sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{5}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x^{4}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{x^{4}x^{2}} - \frac{6*-4sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{6cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}sin(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{2*-4sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{5}} + \frac{2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))}{x^{4}x^{2}} + \frac{2sin(\frac{1}{x})cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}}\\=&\frac{12cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}} + \frac{6sin(xsin(\frac{1}{x}))sin(\frac{1}{x})cos^{2}(\frac{1}{x})}{x^{3}} - \frac{116cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{96cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{90cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin^{3}(\frac{1}{x})} + \frac{56cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{24cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{8}sin^{2}(\frac{1}{x})} - \frac{72sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} - \frac{24cos^{4}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{8}sin^{4}(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} + \frac{14sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{34sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{16cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{24cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{8sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{28cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2cos^{4}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{24sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{9}sin^{5}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{18sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} - \frac{4cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{96sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{8}sin^{4}(\frac{1}{x})} + \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{9}sin^{3}(\frac{1}{x})} - \frac{6sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} + \frac{10sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{9}sin^{3}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{64sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} - \frac{6sin(\frac{1}{x})cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{12cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{4sin(xsin(\frac{1}{x}))sin^{2}(\frac{1}{x})cos(\frac{1}{x})}{x^{2}} + \frac{144sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} + \frac{2sin(\frac{1}{x})cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{3cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}} - \frac{96sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{6sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{16sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{44sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}} + \frac{4sin(xsin(\frac{1}{x}))}{x^{9}sin(\frac{1}{x})} + \frac{3cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{48sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}} - \frac{5cos(xsin(\frac{1}{x}))}{x^{8}} - \frac{24cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{sin(xsin(\frac{1}{x}))sin^{3}(\frac{1}{x})}{x} - \frac{13sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{5}} + \frac{72sin(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))}{x^{9}sin(\frac{1}{x})} - \frac{72cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{4sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{2}} - \frac{4sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}} - \frac{12sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{3}} - \frac{17sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{5}} + \frac{24sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{3sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{7}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sin(xsin(\frac{1}{x})))}{(xsin(\frac{1}{x}))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sin(xsin(\frac{1}{x}))}{xsin(\frac{1}{x})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{sin(xsin(\frac{1}{x}))}{xsin(\frac{1}{x})}\right)}{dx}\\=&\frac{-sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{xsin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{xsin^{2}(\frac{1}{x})x^{2}}\\=&\frac{cos(xsin(\frac{1}{x}))}{x} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cos(xsin(\frac{1}{x}))}{x} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))}{x^{2}sin(\frac{1}{x})}\right)}{dx}\\=&\frac{-cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x} + \frac{-3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{3}(\frac{1}{x})x^{2}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}sin^{2}(\frac{1}{x})x^{2}} - \frac{-2cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}sin^{2}(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}sin(\frac{1}{x})x^{2}} - \frac{-2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{2}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{2}sin^{2}(\frac{1}{x})x^{2}}\\=&\frac{-2cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} - \frac{sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x} + \frac{sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2cos(xsin(\frac{1}{x}))}{x^{2}} + \frac{4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} - \frac{sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x} + \frac{sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{2sin(xsin(\frac{1}{x}))}{x^{3}sin(\frac{1}{x})}\right)}{dx}\\=&\frac{-2*-2cos(xsin(\frac{1}{x}))}{x^{3}} - \frac{2*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{2}} + \frac{4*-3cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{4*-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})x^{2}} + \frac{4*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} + \frac{4cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}sin(\frac{1}{x})x^{2}} - \frac{2*-4cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2*-2cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}sin^{3}(\frac{1}{x})x^{2}} - \frac{2*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{4}sin^{2}(\frac{1}{x})x^{2}} - \frac{2cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}sin^{2}(\frac{1}{x})} + \frac{2*-5sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2*-3cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{4}(\frac{1}{x})x^{2}} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{4*-4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4*-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{3}(\frac{1}{x})x^{2}} - \frac{4cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})} - \frac{4sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{2*-2sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}} + \frac{2sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}x^{2}} - \frac{-3sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{3}sin(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})}{x^{3}sin^{2}(\frac{1}{x})x^{2}} - \frac{sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{3}sin(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x} - \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{xx^{2}} + \frac{-5sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}sin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{-4cos(xsin(\frac{1}{x}))}{x^{5}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}} + \frac{2*-3sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}sin(\frac{1}{x})} + \frac{2sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{3}sin^{2}(\frac{1}{x})x^{2}}\\=& - \frac{cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}} - \frac{18cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{16cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} + \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{18sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{9cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} - \frac{9sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{3sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x} - \frac{9sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{4}} - \frac{6sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{4}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - \frac{cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{3}} - \frac{18cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{16cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}} + \frac{4sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{18sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{9cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} - \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} - \frac{9sin(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})} + \frac{3sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{2}} - \frac{sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x} - \frac{9sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{4}} - \frac{6sin(xsin(\frac{1}{x}))}{x^{4}sin(\frac{1}{x})} + \frac{2sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{4}}\right)}{dx}\\=& - \frac{-3cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{3}} - \frac{cos(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{3}x^{2}} - \frac{18*-4cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} - \frac{18*-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} - \frac{18*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} - \frac{18cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} + \frac{16*-5cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{16*-2cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{16*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{16cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{4*-6cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{4*-cos(\frac{1}{x})*-cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})x^{2}} - \frac{4*-sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{6}sin(\frac{1}{x})x^{2}} - \frac{4cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin(\frac{1}{x})} + \frac{9*-4sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{9sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-cos^{2}(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{9sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} - \frac{6*-6cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin^{3}(\frac{1}{x})} - \frac{6*-3cos(\frac{1}{x})*-cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{4}(\frac{1}{x})x^{2}} - \frac{6*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{6}sin^{3}(\frac{1}{x})x^{2}} - \frac{6cos^{3}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin^{3}(\frac{1}{x})} + \frac{2*-5cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2*-2cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{2*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{6*-7sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{8}sin^{4}(\frac{1}{x})} + \frac{6*-4cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{5}(\frac{1}{x})x^{2}} + \frac{6cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{7}sin^{4}(\frac{1}{x})} + \frac{6sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{7}sin^{4}(\frac{1}{x})x^{2}} - \frac{2*-5sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{2cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{2sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})*-cos^{3}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{2sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{18*-6sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{18*-3cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{4}(\frac{1}{x})x^{2}} - \frac{18cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{2}(\frac{1}{x})}{x^{6}sin^{3}(\frac{1}{x})} - \frac{18sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{6}sin^{3}(\frac{1}{x})x^{2}} + \frac{3*-2sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} + \frac{3cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{2}x^{2}} + \frac{3sin(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{2}} + \frac{3sin(\frac{1}{x})cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{2}x^{2}} + \frac{4*-7sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{4cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} + \frac{4sin(xsin(\frac{1}{x}))*-2cos(\frac{1}{x})*-cos(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})x^{2}} + \frac{4sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{7}sin^{2}(\frac{1}{x})x^{2}} - \frac{-5sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} - \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} - \frac{sin(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} - \frac{2*-3cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{2*-2cos(\frac{1}{x})sin(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{x^{3}x^{2}} - \frac{2cos^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}} + \frac{18*-5sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{18*-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin^{3}(\frac{1}{x})x^{2}} + \frac{18cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{5}sin^{2}(\frac{1}{x})} + \frac{18sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{5}sin^{2}(\frac{1}{x})x^{2}} + \frac{-4cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos^{3}(\frac{1}{x})}{x^{4}sin(\frac{1}{x})} + \frac{cos(xsin(\frac{1}{x}))*-3cos^{2}(\frac{1}{x})sin(\frac{1}{x})*-1}{x^{4}sin(\frac{1}{x})x^{2}} - \frac{-6cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{-cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})x^{2}} - \frac{-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{6}sin(\frac{1}{x})} - \frac{cos(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{6}sin(\frac{1}{x})x^{2}} + \frac{6*-3cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{6*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{3}} + \frac{9*-5cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{9*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{5}} + \frac{-7sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{-2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})x^{2}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{7}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{7}sin^{2}(\frac{1}{x})x^{2}} - \frac{3*-5sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}} - \frac{3cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{5}} - \frac{3sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{5}x^{2}} - \frac{9*-6sin(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{6}sin(\frac{1}{x})} - \frac{9sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{6}sin^{2}(\frac{1}{x})x^{2}} + \frac{3*-2sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{3}} + \frac{3cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x^{2}} + \frac{3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{x^{2}x^{2}} - \frac{-sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{2}} - \frac{2sin(\frac{1}{x})cos(\frac{1}{x})*-cos(xsin(\frac{1}{x}))}{xx^{2}} - \frac{sin^{2}(\frac{1}{x})*-sin(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x} - \frac{9*-3sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}} - \frac{9cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})cos(\frac{1}{x})}{x^{3}} - \frac{9sin(xsin(\frac{1}{x}))*-sin(\frac{1}{x})*-1}{x^{3}x^{2}} + \frac{-4sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{5}} + \frac{cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})sin(\frac{1}{x})}{x^{4}} + \frac{sin(xsin(\frac{1}{x}))cos(\frac{1}{x})*-1}{x^{4}x^{2}} - \frac{6*-4sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{6cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}sin(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))*-cos(\frac{1}{x})*-1}{x^{4}sin^{2}(\frac{1}{x})x^{2}} + \frac{2*-4sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{5}} + \frac{2cos(\frac{1}{x})*-sin(xsin(\frac{1}{x}))}{x^{4}x^{2}} + \frac{2sin(\frac{1}{x})cos(xsin(\frac{1}{x}))(sin(\frac{1}{x}) + \frac{xcos(\frac{1}{x})*-1}{x^{2}})}{x^{4}}\\=&\frac{12cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{4}} + \frac{6sin(xsin(\frac{1}{x}))sin(\frac{1}{x})cos^{2}(\frac{1}{x})}{x^{3}} - \frac{116cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{96cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{90cos^{3}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin^{3}(\frac{1}{x})} + \frac{56cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} - \frac{24cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{8}sin^{2}(\frac{1}{x})} - \frac{72sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} - \frac{24cos^{4}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{8}sin^{4}(\frac{1}{x})} + \frac{6cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} + \frac{14sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{34sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} - \frac{16cos(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{24cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{8sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{28cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2cos^{4}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}sin^{2}(\frac{1}{x})} + \frac{2cos(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{24sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{9}sin^{5}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{18sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{3}} - \frac{4cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} - \frac{96sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{8}sin^{4}(\frac{1}{x})} + \frac{18sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{9}sin^{3}(\frac{1}{x})} - \frac{6sin(\frac{1}{x})cos(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{5}} + \frac{10sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{9}sin^{3}(\frac{1}{x})} - \frac{6sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin(\frac{1}{x})} - \frac{64sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} - \frac{6sin(\frac{1}{x})cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{5}} + \frac{12cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{4sin(xsin(\frac{1}{x}))sin^{2}(\frac{1}{x})cos(\frac{1}{x})}{x^{2}} + \frac{144sin(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{7}sin^{3}(\frac{1}{x})} + \frac{2sin(\frac{1}{x})cos(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{3}} + \frac{3cos(xsin(\frac{1}{x}))cos^{2}(\frac{1}{x})}{x^{6}} - \frac{96sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}sin^{2}(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))cos^{4}(\frac{1}{x})}{x^{5}sin(\frac{1}{x})} + \frac{6sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{4}} - \frac{16sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{8}sin^{2}(\frac{1}{x})} + \frac{44sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{6}} + \frac{4sin(xsin(\frac{1}{x}))}{x^{9}sin(\frac{1}{x})} + \frac{3cos^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{48sin(xsin(\frac{1}{x}))cos(\frac{1}{x})}{x^{4}} - \frac{5cos(xsin(\frac{1}{x}))}{x^{8}} - \frac{24cos(xsin(\frac{1}{x}))}{x^{4}} + \frac{sin(xsin(\frac{1}{x}))sin^{3}(\frac{1}{x})}{x} - \frac{13sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{5}} + \frac{72sin(xsin(\frac{1}{x}))}{x^{7}sin(\frac{1}{x})} + \frac{sin(xsin(\frac{1}{x}))}{x^{9}sin(\frac{1}{x})} - \frac{72cos(xsin(\frac{1}{x}))}{x^{6}} + \frac{4sin^{2}(\frac{1}{x})cos(xsin(\frac{1}{x}))}{x^{2}} - \frac{4sin(xsin(\frac{1}{x}))cos^{3}(\frac{1}{x})}{x^{4}} - \frac{12sin(xsin(\frac{1}{x}))sin(\frac{1}{x})}{x^{3}} - \frac{17sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{5}} + \frac{24sin(xsin(\frac{1}{x}))}{x^{5}sin(\frac{1}{x})} - \frac{3sin(\frac{1}{x})sin(xsin(\frac{1}{x}))}{x^{7}}\\ \end{split}\end{equation} \]
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