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。
\[ \begin{equation}\begin{split}【1/1】求函数ln(sqrt({x}^{2} + 1) - x) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(sqrt(x^{2} + 1) - x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(sqrt(x^{2} + 1) - x)\right)}{dx}\\=&\frac{(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)}\\=&\frac{x}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{1}{2}}} - \frac{1}{(sqrt(x^{2} + 1) - x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{x}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{1}{2}}} - \frac{1}{(sqrt(x^{2} + 1) - x)}\right)}{dx}\\=&\frac{(\frac{-(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{2}})x}{(x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}})x}{(sqrt(x^{2} + 1) - x)} + \frac{1}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{1}{2}}} - (\frac{-(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{2}})\\=&\frac{-x^{2}}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)} + \frac{2x}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{\frac{1}{2}}} - \frac{x^{2}}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{3}{2}}} + \frac{1}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{1}{2}}} - \frac{1}{(sqrt(x^{2} + 1) - x)^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-x^{2}}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)} + \frac{2x}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{\frac{1}{2}}} - \frac{x^{2}}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{3}{2}}} + \frac{1}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{1}{2}}} - \frac{1}{(sqrt(x^{2} + 1) - x)^{2}}\right)}{dx}\\=&\frac{-(\frac{-2(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{3}})x^{2}}{(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{2}}{(sqrt(x^{2} + 1) - x)^{2}} - \frac{2x}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)} + \frac{2(\frac{-2(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{3}})x}{(x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}})x}{(sqrt(x^{2} + 1) - x)^{2}} + \frac{2}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{-(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{2}})x^{2}}{(x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 1)^{\frac{5}{2}}})x^{2}}{(sqrt(x^{2} + 1) - x)} - \frac{2x}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{3}{2}}} + \frac{(\frac{-(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{2}})}{(x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}})}{(sqrt(x^{2} + 1) - x)} - (\frac{-2(\frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} - 1)}{(sqrt(x^{2} + 1) - x)^{3}})\\=&\frac{2x^{3}}{(sqrt(x^{2} + 1) - x)^{3}(x^{2} + 1)^{\frac{3}{2}}} + \frac{3x^{3}}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{2}} - \frac{2x}{(x^{2} + 1)(sqrt(x^{2} + 1) - x)^{2}} - \frac{6x^{2}}{(sqrt(x^{2} + 1) - x)^{3}(x^{2} + 1)} + \frac{6x}{(sqrt(x^{2} + 1) - x)^{3}(x^{2} + 1)^{\frac{1}{2}}} - \frac{3x^{2}}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{\frac{3}{2}}} + \frac{3x^{3}}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{5}{2}}} - \frac{2x}{(x^{2} + 1)^{\frac{3}{2}}(sqrt(x^{2} + 1) - x)} - \frac{x}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)} - \frac{x}{(sqrt(x^{2} + 1) - x)(x^{2} + 1)^{\frac{3}{2}}} + \frac{3}{(sqrt(x^{2} + 1) - x)^{2}(x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(sqrt(x^{2} + 1) - x)^{3}}\\ \end{split}\end{equation} \]