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。
\[ \begin{equation}\begin{split}【1/1】求函数e^{x(e^{x} - 1) - \frac{1}{(2{x}^{2})}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{2}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{-2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{2}} - \frac{3*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{4}} - \frac{2*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} + \frac{-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{6}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 3*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + 2*2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + \frac{3*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x^{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x^{3}} + \frac{2*-2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + 2xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 3x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{4*-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x^{2}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x^{2}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - \frac{6*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{3}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{-e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x} + \frac{2*-e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x} - 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3*-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3*-3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} + \frac{2*-5e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{5}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - \frac{9*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{4}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3*-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{7}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{6}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{-5e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{5}} + \frac{9*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{4}} + \frac{12*-5e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{5}} + \frac{3*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} - \frac{3*-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{6}} - \frac{9*-7e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{7}} + \frac{-9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{10}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{9}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + xe^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 11xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 6e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 8xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + 4x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + 7xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 8e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x^{2}e^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x^{3}e^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + 13x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x^{3}} + \frac{3e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x^{2}} + \frac{8e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x} - \frac{7e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + 2x^{3}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + \frac{5e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + x^{4}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} - \frac{17e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{4e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} - 4xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - \frac{11e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + 2x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{5}} - \frac{14e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{4}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{6}} + \frac{3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} - \frac{25e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + \frac{42e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} + \frac{12e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{8}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{7}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{9}} - \frac{11e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} - \frac{54e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{75e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}} - \frac{48e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} - \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{10}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{12}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{x(e^{x} - 1) - \frac{1}{(2{x}^{2})}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{2*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{2}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{-2e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{2}} - \frac{3*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{4}} - \frac{2*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} + \frac{-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{6}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}}\right)}{dx}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 3*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + 2*2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{3}} + 2x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*3e^{{x}*{2}}e^{x} + \frac{3*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x^{3}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x^{3}} + \frac{2*-2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{2*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{2}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + 2xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + 3x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}*3e^{{x}*{2}}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) + \frac{4*-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x^{2}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x^{2}} + 2xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}*2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - \frac{6*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{3}} - \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} + \frac{-e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{2e^{x}e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x} + \frac{2*-e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}}}{x} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x}}{x} - 2xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{{x}*{2}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}*2e^{x}e^{x} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x} + xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} - \frac{3*-2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{2}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} - \frac{3*-3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} - \frac{3e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} + \frac{2*-5e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{5}} + \frac{2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}}) - \frac{9*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{4}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{3*-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{7}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})e^{x}}{x^{6}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} + \frac{-5e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{5}} + \frac{9*-4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{4}} + \frac{12*-5e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{12e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{5}} + \frac{3*-3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{3}} - \frac{3*-6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{6}} - \frac{9*-7e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{7}} + \frac{-9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{10}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}(e^{x} + xe^{x} - 1 - \frac{\frac{1}{2}*-2}{x^{3}})}{x^{9}}\\=&e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + xe^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 11xe^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 6e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 8xe^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 3xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + 4x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + 7xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} - x^{2}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}} + 8e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x^{2}e^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + 2x^{3}e^{{x}*{4}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - 2e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} + 13x^{2}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x^{3}} + \frac{3e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x^{2}} + \frac{8e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{3}}}{x} - \frac{7e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + 2x^{3}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} + \frac{5e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{2}} + x^{4}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{4}} - \frac{17e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{3}} + \frac{4e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} - 4xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}} - \frac{11e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{2}} + 2x^{3}e^{{x}*{3}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{9e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{5}} - \frac{14e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{4}} + x^{2}e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} + \frac{6e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x^{6}} + \frac{3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x} + \frac{2e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{{x}*{2}}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} + \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{4}} + \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{3}} - \frac{25e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{6}} - \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{{x}*{2}}}{x} - xe^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{2}} + \frac{42e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{5}} + \frac{12e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} + \frac{3e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{8}} + e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}} - \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{7}} + \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}e^{x}}{x^{9}} - \frac{11e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{e^{x}e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{4}} - \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{3}} + \frac{36e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{7}} - \frac{54e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{6}} + \frac{75e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{8}} - \frac{4e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{9}} - \frac{48e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{5}} - \frac{18e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{10}} + \frac{e^{xe^{x} - x - \frac{\frac{1}{2}}{x^{2}}}}{x^{12}}\\ \end{split}\end{equation} \]
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