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 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(\frac{(2 - x)}{(5 - x)})}{(1 - {(\frac{(2 - x)}{(5 - x)})}^{2})} - \frac{(\frac{(2 + x)}{(5 + x)})}{(1 - {(\frac{(2 + x)}{(5 + x)})}^{2})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-x}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{x}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} + \frac{2}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{2}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-x}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{x}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} + \frac{2}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{2}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)}\right)}{dx}\\=&\frac{-(\frac{-(-1 + 0)}{(-x + 5)^{2}})x}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{(\frac{-(-(\frac{-2(-1 + 0)}{(-x + 5)^{3}})x^{2} - \frac{2x}{(-x + 5)^{2}} + 4(\frac{-2(-1 + 0)}{(-x + 5)^{3}})x + \frac{4}{(-x + 5)^{2}} - 4(\frac{-2(-1 + 0)}{(-x + 5)^{3}}) + 0)}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}})x}{(-x + 5)} - \frac{1}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{(\frac{-(1 + 0)}{(x + 5)^{2}})x}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} - \frac{(\frac{-(-(\frac{-2(1 + 0)}{(x + 5)^{3}})x^{2} - \frac{2x}{(x + 5)^{2}} - 4(\frac{-2(1 + 0)}{(x + 5)^{3}})x - \frac{4}{(x + 5)^{2}} - 4(\frac{-2(1 + 0)}{(x + 5)^{3}}) + 0)}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}})x}{(x + 5)} - \frac{1}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} + \frac{2(\frac{-(-1 + 0)}{(-x + 5)^{2}})}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} + \frac{2(\frac{-(-(\frac{-2(-1 + 0)}{(-x + 5)^{3}})x^{2} - \frac{2x}{(-x + 5)^{2}} + 4(\frac{-2(-1 + 0)}{(-x + 5)^{3}})x + \frac{4}{(-x + 5)^{2}} - 4(\frac{-2(-1 + 0)}{(-x + 5)^{3}}) + 0)}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}})}{(-x + 5)} - \frac{2(\frac{-(1 + 0)}{(x + 5)^{2}})}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} - \frac{2(\frac{-(-(\frac{-2(1 + 0)}{(x + 5)^{3}})x^{2} - \frac{2x}{(x + 5)^{2}} - 4(\frac{-2(1 + 0)}{(x + 5)^{3}})x - \frac{4}{(x + 5)^{2}} - 4(\frac{-2(1 + 0)}{(x + 5)^{3}}) + 0)}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}})}{(x + 5)}\\=&\frac{-x}{(-x + 5)^{2}(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{2x^{3}}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{4}} - \frac{2x^{2}}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{3}} + \frac{12x^{2}}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{4}} - \frac{2x^{2}}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{3}} + \frac{2x^{3}}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{4}} + \frac{x}{(x + 5)^{2}(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} + \frac{12x^{2}}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{4}} + \frac{8x}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{3}} - \frac{24x}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{4}} - \frac{8x}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{3}} + \frac{24x}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{4}} + \frac{2}{(-x + 5)^{2}(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} + \frac{2}{(x + 5)^{2}(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} - \frac{1}{(-x + 5)(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)} - \frac{1}{(x + 5)(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)} + \frac{16}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{4}} + \frac{16}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{4}} - \frac{8}{(\frac{-x^{2}}{(x + 5)^{2}} - \frac{4x}{(x + 5)^{2}} - \frac{4}{(x + 5)^{2}} + 1)^{2}(x + 5)^{3}} - \frac{8}{(\frac{-x^{2}}{(-x + 5)^{2}} + \frac{4x}{(-x + 5)^{2}} - \frac{4}{(-x + 5)^{2}} + 1)^{2}(-x + 5)^{3}}\\ \end{split}\end{equation} \]
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