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。
\[ \begin{equation}\begin{split}【1/1】求函数({(1 + x)}^{\frac{1}{x}}{(1 + \frac{1}{x})}^{x} - 4){\frac{1}{(x - 1)}}^{2} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}} - \frac{4}{(x - 1)^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}} - \frac{4}{(x - 1)^{2}}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x - 1)^{3}})(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}} + \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}} + \frac{(\frac{1}{x} + 1)^{x}((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))}{(x - 1)^{2}} - 4(\frac{-2(1 + 0)}{(x - 1)^{3}})\\=&\frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{2}} - \frac{2(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{3}} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)x} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}x^{2}} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(x + 1)x} + \frac{8}{(x - 1)^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{2}} - \frac{2(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{3}} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)x} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}x^{2}} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(x + 1)x} + \frac{8}{(x - 1)^{3}}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x - 1)^{3}})(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1) + \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{2}} + \frac{(\frac{1}{x} + 1)^{x}((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))ln(\frac{1}{x} + 1)}{(x - 1)^{2}} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}(\frac{-1}{x^{2}} + 0)}{(x - 1)^{2}(\frac{1}{x} + 1)} - 2(\frac{-3(1 + 0)}{(x - 1)^{4}})(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}} - \frac{2((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))(x + 1)^{\frac{1}{x}}}{(x - 1)^{3}} - \frac{2(\frac{1}{x} + 1)^{x}((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))}{(x - 1)^{3}} - \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(\frac{1}{x} + 1)x} - \frac{(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}x} - \frac{-(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)x^{2}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)x} - \frac{(\frac{1}{x} + 1)^{x}((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))}{(x - 1)^{2}(\frac{1}{x} + 1)x} - \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{x^{2}} - \frac{-2(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}x^{3}} - \frac{((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}x^{2}} - \frac{(x + 1)^{\frac{1}{x}}((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(x + 1)}{(x - 1)^{2}x^{2}} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}(1 + 0)}{(x - 1)^{2}x^{2}(x + 1)} + \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x + 1)x} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}x} + \frac{-(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(x + 1)x^{2}} + \frac{((x + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + 1) + \frac{(\frac{1}{x})(1 + 0)}{(x + 1)}))(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(x + 1)x} + \frac{(x + 1)^{\frac{1}{x}}((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(x - 1)^{2}(x + 1)x} + 8(\frac{-3(1 + 0)}{(x - 1)^{4}})\\=&\frac{-4(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{3}} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln^{2}(\frac{1}{x} + 1)}{(x - 1)^{2}} - \frac{2(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{2}(\frac{1}{x} + 1)x} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)ln(\frac{1}{x} + 1)}{(x - 1)^{2}x^{2}} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(x - 1)^{2}(x + 1)x} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)ln(x + 1)}{(x - 1)^{2}x^{2}} + \frac{6(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{4}} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}(\frac{1}{x} + 1)x^{3}} - \frac{2(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}(x + 1)x^{3}} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(x + 1)}{(x - 1)^{2}(\frac{1}{x} + 1)x^{3}} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}ln(\frac{1}{x} + 1)}{(x - 1)^{2}(x + 1)x} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)^{2}x^{2}} + \frac{4(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{3}(\frac{1}{x} + 1)x} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(\frac{1}{x} + 1)(x + 1)x^{2}} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)x^{2}} + \frac{2(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{2}x^{3}} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln^{2}(x + 1)}{(x - 1)^{2}x^{4}} - \frac{4(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{3}(x + 1)x} + \frac{4(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}ln(x + 1)}{(x - 1)^{3}x^{2}} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(\frac{1}{x} + 1)^{2}x^{3}} - \frac{2(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x + 1)(x - 1)^{2}x^{2}} - \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x + 1)^{2}(x - 1)^{2}x} + \frac{(x + 1)^{\frac{1}{x}}(\frac{1}{x} + 1)^{x}}{(x - 1)^{2}(x + 1)^{2}x^{2}} + \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(\frac{1}{x} + 1)(x - 1)^{2}x^{2}} - \frac{(\frac{1}{x} + 1)^{x}(x + 1)^{\frac{1}{x}}}{(x - 1)^{2}(x + 1)(\frac{1}{x} + 1)x^{2}} - \frac{24}{(x - 1)^{4}}\\ \end{split}\end{equation} \]
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