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 a 求 2 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数a{\frac{1}{(rr + aa)}}^{\frac{3}{2}} - (h - a){\frac{1}{(rr + (h - a)(h - a))}}^{\frac{3}{2}} 关于 a 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{a}{(r^{2} + a^{2})^{\frac{3}{2}}} - \frac{h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}} + \frac{a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{a}{(r^{2} + a^{2})^{\frac{3}{2}}} - \frac{h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}} + \frac{a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\right)}{da}\\=&(\frac{\frac{-3}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{5}{2}}})a + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})h + 0 + (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})a + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\=&\frac{-3a^{2}}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{6ha}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3h^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3a^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-3a^{2}}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{6ha}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3h^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3a^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\right)}{da}\\=&-3(\frac{\frac{-5}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{7}{2}}})a^{2} - \frac{3*2a}{(r^{2} + a^{2})^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})ha + \frac{6h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - 3(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})h^{2} + 0 - 3(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})a^{2} - \frac{3*2a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{5}{2}}}) + (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})\\=&\frac{15a^{3}}{(r^{2} + a^{2})^{\frac{7}{2}}} - \frac{9a}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{45h^{2}a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} - \frac{45ha^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} + \frac{9h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{15h^{3}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} + \frac{15a^{3}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} - \frac{9a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数a{\frac{1}{(rr + aa)}}^{\frac{3}{2}} - (h - a){\frac{1}{(rr + (h - a)(h - a))}}^{\frac{3}{2}} 关于 a 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{a}{(r^{2} + a^{2})^{\frac{3}{2}}} - \frac{h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}} + \frac{a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{a}{(r^{2} + a^{2})^{\frac{3}{2}}} - \frac{h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}} + \frac{a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\right)}{da}\\=&(\frac{\frac{-3}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{5}{2}}})a + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})h + 0 + (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})a + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\=&\frac{-3a^{2}}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{6ha}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3h^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3a^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-3a^{2}}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{6ha}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3h^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{3a^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + \frac{1}{(r^{2} + a^{2})^{\frac{3}{2}}} + \frac{1}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{3}{2}}}\right)}{da}\\=&-3(\frac{\frac{-5}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{7}{2}}})a^{2} - \frac{3*2a}{(r^{2} + a^{2})^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})ha + \frac{6h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - 3(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})h^{2} + 0 - 3(\frac{\frac{-5}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}})a^{2} - \frac{3*2a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(0 + 2a)}{(r^{2} + a^{2})^{\frac{5}{2}}}) + (\frac{\frac{-3}{2}(0 - 2h + 0 + 2a)}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}})\\=&\frac{15a^{3}}{(r^{2} + a^{2})^{\frac{7}{2}}} - \frac{9a}{(r^{2} + a^{2})^{\frac{5}{2}}} + \frac{45h^{2}a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} - \frac{45ha^{2}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} + \frac{9h}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}} - \frac{15h^{3}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} + \frac{15a^{3}}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{7}{2}}} - \frac{9a}{(r^{2} - 2ha + h^{2} + a^{2})^{\frac{5}{2}}}\\ \end{split}\end{equation} \]
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