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 3 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数ln(\frac{(1 - x)}{(1 + x)}) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})\right)}{dx}\\=&\frac{(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})}\\=&\frac{x}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})(x + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{x}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})(x + 1)}\right)}{dx}\\=&\frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} + \frac{(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})x}{(x + 1)^{2}} + \frac{1}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})}{(x + 1)^{2}} - \frac{(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})}{(x + 1)} - \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})}\\=&\frac{-2x}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{x^{2}}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{x}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} + \frac{2}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2x}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{x^{2}}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{x}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} + \frac{2}{(x + 1)^{2}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{1}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} - \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{2}}\right)}{dx}\\=&\frac{-2(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{2(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})x}{(x + 1)^{3}} - \frac{2}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{(\frac{-4(1 + 0)}{(x + 1)^{5}})x^{2}}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})x^{2}}{(x + 1)^{4}} - \frac{2x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})x}{(x + 1)^{3}} + \frac{1}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2(\frac{-4(1 + 0)}{(x + 1)^{5}})x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{2(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})x}{(x + 1)^{4}} + \frac{2}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})x}{(x + 1)^{3}} + \frac{(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} + \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} + \frac{2(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})}{(x + 1)^{2}} - \frac{(\frac{-4(1 + 0)}{(x + 1)^{5}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})}{(x + 1)^{4}} + \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} + \frac{2(\frac{-(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}})}{(x + 1)^{3}} - \frac{(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})}{(x + 1)^{3}} - \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})}{(x + 1)^{3}} - \frac{(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{(\frac{-2(-(\frac{-(1 + 0)}{(x + 1)^{2}})x - \frac{1}{(x + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}})}{(x + 1)^{2}} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}}\\=&\frac{6x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} + \frac{6x^{2}}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{10x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{12x}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{2x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{4}} + \frac{2x^{3}}{(x + 1)^{6}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{4x^{2}}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{6x^{2}}{(x + 1)^{6}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{2x^{2}}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{5}} + \frac{2x}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} + \frac{8x}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} + \frac{6x}{(x + 1)^{6}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} + \frac{4x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{4}} + \frac{4x}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{5}} + \frac{1}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}(x + 1)^{3}} + \frac{12}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{6}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} + \frac{5}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{2}} - \frac{2}{(x + 1)^{6}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{6}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{6}{(x + 1)^{3}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})} - \frac{4}{(x + 1)^{5}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{2}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{5}} - \frac{4}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{4}} - \frac{2}{(x + 1)^{4}(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}} - \frac{2}{(\frac{-x}{(x + 1)} + \frac{1}{(x + 1)})^{3}(x + 1)^{3}}\\ \end{split}\end{equation} \]
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