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 5 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{2(x + 1 - {e}^{x})}{(ln(x + 1) - x)} 关于 x 的 5 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2x}{(ln(x + 1) - x)} - \frac{2{e}^{x}}{(ln(x + 1) - x)} + \frac{2}{(ln(x + 1) - x)}\\\\ &\color{blue}{函数的 5 阶导数：} \\=&\frac{-480x}{(x + 1)^{5}(ln(x + 1) - x)^{5}} - \frac{2{e}^{x}}{(ln(x + 1) - x)} + \frac{1440x}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{10{e}^{x}}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{420x}{(x + 1)^{5}(ln(x + 1) - x)^{4}} - \frac{10{e}^{x}}{(ln(x + 1) - x)^{2}} - \frac{40{e}^{x}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{660x}{(x + 1)^{4}(ln(x + 1) - x)^{4}} + \frac{80{e}^{x}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{20{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{200x}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{40{e}^{x}}{(ln(x + 1) - x)^{3}} + \frac{120{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{360{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{280{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{120x}{(x + 1)^{4}(ln(x + 1) - x)^{3}} + \frac{360{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{120{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{40{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{48x}{(x + 1)^{5}(ln(x + 1) - x)^{2}} + \frac{1200x}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{120{e}^{x}}{(ln(x + 1) - x)^{4}} - \frac{2400x}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{2400x}{(ln(x + 1) - x)^{6}(x + 1)^{2}} - \frac{1440x}{(x + 1)^{3}(ln(x + 1) - x)^{5}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{960{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{1020{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{4}} - \frac{1200x}{(ln(x + 1) - x)^{6}(x + 1)} + \frac{480x}{(x + 1)^{2}(ln(x + 1) - x)^{5}} - \frac{240x}{(x + 1)^{3}(ln(x + 1) - x)^{4}} + \frac{960{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{4}} - \frac{1440{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{2}} - \frac{340{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{3}} + \frac{960{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)} - \frac{360{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{4}} - \frac{60{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{2}} - \frac{240x}{(ln(x + 1) - x)^{6}(x + 1)^{5}} + \frac{240x}{(ln(x + 1) - x)^{6}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{5}} + \frac{480{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{5}} + \frac{240{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{5}} - \frac{1200{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{1440{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{420{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{4}} + \frac{2400{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{1440{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{5}} + \frac{200{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{2400{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{2}} + \frac{48{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{2}} - \frac{480{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{5}} + \frac{1200{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)} - \frac{420}{(x + 1)^{5}(ln(x + 1) - x)^{4}} + \frac{240}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{1440}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{1020}{(x + 1)^{4}(ln(x + 1) - x)^{4}} - \frac{960}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{200}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{1440}{(x + 1)^{3}(ln(x + 1) - x)^{5}} - \frac{480}{(x + 1)^{5}(ln(x + 1) - x)^{5}} - \frac{48}{(x + 1)^{5}(ln(x + 1) - x)^{2}} + \frac{340}{(x + 1)^{4}(ln(x + 1) - x)^{3}} - \frac{960}{(x + 1)^{3}(ln(x + 1) - x)^{4}} + \frac{1440}{(ln(x + 1) - x)^{5}(x + 1)^{2}} + \frac{480}{(x + 1)^{2}(ln(x + 1) - x)^{5}} - \frac{160}{(x + 1)^{3}(ln(x + 1) - x)^{3}} - \frac{240}{(ln(x + 1) - x)^{6}(x + 1)^{5}} - \frac{960}{(ln(x + 1) - x)^{5}(x + 1)} + \frac{360}{(x + 1)^{2}(ln(x + 1) - x)^{4}} + \frac{60}{(x + 1)^{4}(ln(x + 1) - x)^{2}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{6}} + \frac{1200}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{2400}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{2400}{(ln(x + 1) - x)^{6}(x + 1)^{2}} - \frac{1200}{(ln(x + 1) - x)^{6}(x + 1)} + \frac{240}{(ln(x + 1) - x)^{5}} + \frac{240}{(ln(x + 1) - x)^{6}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{2(x + 1 - {e}^{x})}{(ln(x + 1) - x)} 关于 x 的 5 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2x}{(ln(x + 1) - x)} - \frac{2{e}^{x}}{(ln(x + 1) - x)} + \frac{2}{(ln(x + 1) - x)}\\\\ &\color{blue}{函数的 5 阶导数：} \\=&\frac{-480x}{(x + 1)^{5}(ln(x + 1) - x)^{5}} - \frac{2{e}^{x}}{(ln(x + 1) - x)} + \frac{1440x}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{10{e}^{x}}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{420x}{(x + 1)^{5}(ln(x + 1) - x)^{4}} - \frac{10{e}^{x}}{(ln(x + 1) - x)^{2}} - \frac{40{e}^{x}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{660x}{(x + 1)^{4}(ln(x + 1) - x)^{4}} + \frac{80{e}^{x}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{20{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{200x}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{40{e}^{x}}{(ln(x + 1) - x)^{3}} + \frac{120{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{360{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{280{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{120x}{(x + 1)^{4}(ln(x + 1) - x)^{3}} + \frac{360{e}^{x}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{120{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{40{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{48x}{(x + 1)^{5}(ln(x + 1) - x)^{2}} + \frac{1200x}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{120{e}^{x}}{(ln(x + 1) - x)^{4}} - \frac{2400x}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{2400x}{(ln(x + 1) - x)^{6}(x + 1)^{2}} - \frac{1440x}{(x + 1)^{3}(ln(x + 1) - x)^{5}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{960{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{1020{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{4}} - \frac{1200x}{(ln(x + 1) - x)^{6}(x + 1)} + \frac{480x}{(x + 1)^{2}(ln(x + 1) - x)^{5}} - \frac{240x}{(x + 1)^{3}(ln(x + 1) - x)^{4}} + \frac{960{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{4}} - \frac{1440{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)^{2}} - \frac{340{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{3}} + \frac{960{e}^{x}}{(ln(x + 1) - x)^{5}(x + 1)} - \frac{360{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{4}} - \frac{60{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{2}} - \frac{240x}{(ln(x + 1) - x)^{6}(x + 1)^{5}} + \frac{240x}{(ln(x + 1) - x)^{6}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{5}} + \frac{480{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{5}} + \frac{240{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{5}} - \frac{1200{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{1440{e}^{x}}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{420{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{4}} + \frac{2400{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{1440{e}^{x}}{(x + 1)^{3}(ln(x + 1) - x)^{5}} + \frac{200{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{2400{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)^{2}} + \frac{48{e}^{x}}{(x + 1)^{5}(ln(x + 1) - x)^{2}} - \frac{480{e}^{x}}{(x + 1)^{2}(ln(x + 1) - x)^{5}} + \frac{1200{e}^{x}}{(ln(x + 1) - x)^{6}(x + 1)} - \frac{420}{(x + 1)^{5}(ln(x + 1) - x)^{4}} + \frac{240}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{1440}{(x + 1)^{4}(ln(x + 1) - x)^{5}} + \frac{1020}{(x + 1)^{4}(ln(x + 1) - x)^{4}} - \frac{960}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{200}{(x + 1)^{5}(ln(x + 1) - x)^{3}} - \frac{1440}{(x + 1)^{3}(ln(x + 1) - x)^{5}} - \frac{480}{(x + 1)^{5}(ln(x + 1) - x)^{5}} - \frac{48}{(x + 1)^{5}(ln(x + 1) - x)^{2}} + \frac{340}{(x + 1)^{4}(ln(x + 1) - x)^{3}} - \frac{960}{(x + 1)^{3}(ln(x + 1) - x)^{4}} + \frac{1440}{(ln(x + 1) - x)^{5}(x + 1)^{2}} + \frac{480}{(x + 1)^{2}(ln(x + 1) - x)^{5}} - \frac{160}{(x + 1)^{3}(ln(x + 1) - x)^{3}} - \frac{240}{(ln(x + 1) - x)^{6}(x + 1)^{5}} - \frac{960}{(ln(x + 1) - x)^{5}(x + 1)} + \frac{360}{(x + 1)^{2}(ln(x + 1) - x)^{4}} + \frac{60}{(x + 1)^{4}(ln(x + 1) - x)^{2}} - \frac{240{e}^{x}}{(ln(x + 1) - x)^{6}} + \frac{1200}{(ln(x + 1) - x)^{6}(x + 1)^{4}} - \frac{2400}{(ln(x + 1) - x)^{6}(x + 1)^{3}} + \frac{2400}{(ln(x + 1) - x)^{6}(x + 1)^{2}} - \frac{1200}{(ln(x + 1) - x)^{6}(x + 1)} + \frac{240}{(ln(x + 1) - x)^{5}} + \frac{240}{(ln(x + 1) - x)^{6}}\\ \end{split}\end{equation} \]
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