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