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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{({x}^{3} - 3x)}{(x - arctan(x))} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{3}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{3}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))}\right)}{dx}\\=&(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x^{3} + \frac{3x^{2}}{(x - arctan(x))} - 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x - \frac{3}{(x - arctan(x))}\\=&\frac{x^{3}}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{3x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{x^{3}}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{3x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))}\right)}{dx}\\=&\frac{(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x^{3}}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)} - (\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x^{3} - \frac{3x^{2}}{(x - arctan(x))^{2}} + 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x^{2} + \frac{3*2x}{(x - arctan(x))} - \frac{3(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x}{(x^{2} + 1)} - \frac{3(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))^{2}(x^{2} + 1)} + 3(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x + \frac{3}{(x - arctan(x))^{2}} - 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})\\=&\frac{2x^{3}}{(x - arctan(x))^{3}(x^{2} + 1)^{2}} - \frac{4x^{3}}{(x - arctan(x))^{3}(x^{2} + 1)} - \frac{2x^{4}}{(x - arctan(x))^{2}(x^{2} + 1)^{2}} + \frac{3x^{2}}{(x^{2} + 1)(x - arctan(x))^{2}} + \frac{2x^{3}}{(x - arctan(x))^{3}} - \frac{6x^{2}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{6x}{(x - arctan(x))} - \frac{6x}{(x - arctan(x))^{3}(x^{2} + 1)^{2}} + \frac{12x}{(x - arctan(x))^{3}(x^{2} + 1)} + \frac{6x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)^{2}} - \frac{6}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{6x}{(x - arctan(x))^{3}} + \frac{6}{(x - arctan(x))^{2}}\\ \end{split}\end{equation} \]