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。
\[ \begin{equation}\begin{split}【1/1】求函数(xx + e^{1 - x} - x){\frac{1}{(({x}^{2}{x}^{2} + {(1 - x)}^{2}{x}^{2}))}}^{\frac{1}{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x^{2} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} + \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\=& - \frac{4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{4x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{7x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - \frac{4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{4x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{7x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=& - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} - \frac{4*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} + \frac{3*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 2(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{5} - \frac{4*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 7(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{4} + \frac{7*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} - \frac{4*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})\\=&\frac{48x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{8xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{28x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{38x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{17x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{48x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{123x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{69x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{21x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{3x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{3x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{48x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{8xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{28x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{38x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{17x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{48x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{123x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{69x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{21x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{3x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{3x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&48(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6}e^{-x + 1} + \frac{48*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{48x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 72(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5}e^{-x + 1} - \frac{72*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 51(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4}e^{-x + 1} + \frac{51*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 18(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} - \frac{18*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 8(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} + \frac{8*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 18(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3}e^{-x + 1} - \frac{18*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 8(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} + \frac{8e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 3(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2}e^{-x + 1} + \frac{3*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{3x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 28(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{4} - \frac{28*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 38(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} + \frac{38*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 17(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} - \frac{17*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 48(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{8} + \frac{48*8x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 120(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{7} - \frac{120*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 123(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6} + \frac{123*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 69(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5} - \frac{69*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 21(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4} + \frac{21*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} + \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 3(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3} - \frac{3*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 2(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})\\=&\frac{-960x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{648x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1485x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{693x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{585x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{360x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{45xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{135x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{15x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{720x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{1548x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1368x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{648x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{120x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{162x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{36x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{960x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3120x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{4500x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3825x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2070x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{720x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{150x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{18x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{15x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-960x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{648x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1485x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{693x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{585x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{360x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{45xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{135x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{15x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{720x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{1548x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1368x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{648x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{120x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{162x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{36x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{960x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3120x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{4500x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3825x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2070x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{720x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{150x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{18x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{15x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\right)}{dx}\\=&-960(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{9}e^{-x + 1} - \frac{960*9x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{960x^{9}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 2160(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{8}e^{-x + 1} + \frac{2160*8x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 2340(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{7}e^{-x + 1} - \frac{2340*7x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 648(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5}e^{-x + 1} + \frac{648*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{648x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 144(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6}e^{-x + 1} - \frac{144*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 1485(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{6}e^{-x + 1} + \frac{1485*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{1485x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 693(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4}e^{-x + 1} - \frac{693*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{693x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 585(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{5}e^{-x + 1} - \frac{585*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{585x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 360(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3}e^{-x + 1} + \frac{360*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{360x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 45(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} - \frac{45e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{45xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 45(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} + \frac{45*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 12(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} - \frac{12*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 135(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{4}e^{-x + 1} + \frac{135*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{135x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 90(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2}e^{-x + 1} - \frac{90*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{90x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 9(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})e^{-x + 1} + \frac{9e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 15(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{3}e^{-x + 1} - \frac{15*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{15x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 9(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})xe^{-x + 1} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 720(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{7} + \frac{720*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 1548(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6} - \frac{1548*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 1368(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5} + \frac{1368*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 120(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} - \frac{120*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 648(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4} - \frac{648*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 120(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} + \frac{120*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 162(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3} + \frac{162*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 36(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x - \frac{36}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 960(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{11} - \frac{960*11x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3120(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{10} + \frac{3120*10x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 4500(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{9} - \frac{4500*9x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3825(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{8} + \frac{3825*8x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 2070(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{7} - \frac{2070*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 720(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{6} + \frac{720*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 150(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{5} - \frac{150*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - 18(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2} - \frac{18*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 15(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{4} + \frac{15*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})\\=&\frac{26880x^{12}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{80640x^{11}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{117600x^{10}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{25920x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3840x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{105840x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{43920x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{63945x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{38700x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{4914x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{2160x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{288x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{26460x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{20160x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{3780x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{7350x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{6390x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{1386x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{54e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{136xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{84x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{16x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1260x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{1140x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{216xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{105x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{24960x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{72960x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{94680x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{6480x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{71820x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{11808x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{34290x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{8712x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{360x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{10350x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{3312x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{240x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1830x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{621x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{26880x^{14}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{107520x^{13}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{198240x^{12}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{223440x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{169785x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{90405x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{33810x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{8610x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{1365x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{45x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{150x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{105x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{36}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(xx + e^{1 - x} - x){\frac{1}{(({x}^{2}{x}^{2} + {(1 - x)}^{2}{x}^{2}))}}^{\frac{1}{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x^{2} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} + \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\=& - \frac{4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{4x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{7x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - \frac{4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{4x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{7x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=& - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} - \frac{4*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{4x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} + \frac{3*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 2(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})x + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{5} - \frac{4*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 7(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{4} + \frac{7*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 4(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} - \frac{4*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} + \frac{2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})\\=&\frac{48x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{8xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{28x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{38x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{17x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{48x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{123x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{69x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{21x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{3x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{3x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{48x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{8xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{28x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{38x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{17x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{48x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{123x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{69x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{21x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + \frac{3x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{3x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{2}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&48(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6}e^{-x + 1} + \frac{48*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{48x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 72(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5}e^{-x + 1} - \frac{72*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{72x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 51(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4}e^{-x + 1} + \frac{51*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{51x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 18(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} - \frac{18*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{18x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 8(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} + \frac{8*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 18(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3}e^{-x + 1} - \frac{18*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{18x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 8(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} + \frac{8e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{8xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 3(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2}e^{-x + 1} + \frac{3*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{3x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - (\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 28(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{4} - \frac{28*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 38(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} + \frac{38*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 17(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} - \frac{17*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 48(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{8} + \frac{48*8x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 120(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{7} - \frac{120*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 123(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6} + \frac{123*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 69(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5} - \frac{69*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 21(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4} + \frac{21*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} + \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 3(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3} - \frac{3*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 2(\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})\\=&\frac{-960x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{648x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1485x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{693x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{585x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{360x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{45xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{135x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{15x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{720x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{1548x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1368x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{648x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{120x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{162x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{36x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{960x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3120x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{4500x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3825x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2070x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{720x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{150x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{18x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{15x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-960x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{648x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1485x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{693x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{585x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{360x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{45xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{135x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{15x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{720x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{1548x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{1368x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{120x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{648x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{120x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{162x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{36x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{960x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3120x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{4500x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3825x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2070x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{720x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{150x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{18x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{15x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\right)}{dx}\\=&-960(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{9}e^{-x + 1} - \frac{960*9x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{960x^{9}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 2160(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{8}e^{-x + 1} + \frac{2160*8x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{2160x^{8}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 2340(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{7}e^{-x + 1} - \frac{2340*7x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{2340x^{7}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 648(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5}e^{-x + 1} + \frac{648*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{648x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 144(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6}e^{-x + 1} - \frac{144*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{144x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 1485(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{6}e^{-x + 1} + \frac{1485*6x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{1485x^{6}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 693(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4}e^{-x + 1} - \frac{693*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{693x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 585(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{5}e^{-x + 1} - \frac{585*5x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{585x^{5}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 360(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3}e^{-x + 1} + \frac{360*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{360x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 45(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})xe^{-x + 1} - \frac{45e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{45xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 45(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2}e^{-x + 1} + \frac{45*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{45x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 12(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3}e^{-x + 1} - \frac{12*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{12x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 135(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{4}e^{-x + 1} + \frac{135*4x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{135x^{4}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 90(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2}e^{-x + 1} - \frac{90*2xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{90x^{2}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 9(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})e^{-x + 1} + \frac{9e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 15(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{3}e^{-x + 1} - \frac{15*3x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{15x^{3}e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 9(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})xe^{-x + 1} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{9xe^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 720(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{7} + \frac{720*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 1548(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{6} - \frac{1548*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 1368(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{5} + \frac{1368*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 120(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{3} - \frac{120*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 648(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{4} - \frac{648*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 120(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x^{2} + \frac{120*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + 162(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{3} + \frac{162*3x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - 36(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})x - \frac{36}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - 960(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{11} - \frac{960*11x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3120(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{10} + \frac{3120*10x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 4500(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{9} - \frac{4500*9x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3825(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{8} + \frac{3825*8x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 2070(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{7} - \frac{2070*7x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 720(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{6} + \frac{720*6x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - 150(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{5} - \frac{150*5x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - (\frac{\frac{-1}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}})e^{-x + 1} - \frac{e^{-x + 1}(-1 + 0)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - 18(\frac{\frac{-5}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}})x^{2} - \frac{18*2x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + 15(\frac{\frac{-7}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}})x^{4} + \frac{15*4x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + 3(\frac{\frac{-3}{2}(2*4x^{3} - 2*3x^{2} + 2x)}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}})\\=&\frac{26880x^{12}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{80640x^{11}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{117600x^{10}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{25920x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{3840x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{105840x^{9}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{43920x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{63945x^{8}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{38700x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{4914x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{2160x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{288x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{26460x^{7}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{20160x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{3780x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{7350x^{6}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{6390x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{1386x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{54e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{136xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{84x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{16x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1260x^{5}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{1140x^{3}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{216xe^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{105x^{4}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{90x^{2}e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{9e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{24960x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{72960x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{94680x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{6480x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{71820x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{11808x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{34290x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{8712x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} - \frac{360x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} + \frac{10350x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{3312x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{240x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}} - \frac{1830x^{4}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} + \frac{621x^{2}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{26880x^{14}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{107520x^{13}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{198240x^{12}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{223440x^{11}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{169785x^{10}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{90405x^{9}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{33810x^{8}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{8610x^{7}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{1365x^{6}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} + \frac{e^{-x + 1}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{1}{2}}} - \frac{45x}{(2x^{4} - 2x^{3} + x^{2})^{\frac{5}{2}}} + \frac{150x^{3}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{7}{2}}} - \frac{105x^{5}}{(2x^{4} - 2x^{3} + x^{2})^{\frac{9}{2}}} - \frac{36}{(2x^{4} - 2x^{3} + x^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]
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