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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{sqrt({(40 - x)}^{2} + {30}^{2})}{sqrt({(40 + x)}^{2} + {30}^{2})} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sqrt(x^{2} - 80x + 2500)}{sqrt(x^{2} + 80x + 2500)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{sqrt(x^{2} - 80x + 2500)}{sqrt(x^{2} + 80x + 2500)}\right)}{dx}\\=&\frac{(2x - 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{sqrt(x^{2} - 80x + 2500)*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}}\\=&\frac{x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{40}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{40sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{40}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{40sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(2x - 80 + 0)}{(x^{2} - 80x + 2500)^{\frac{3}{2}}})x}{sqrt(x^{2} + 80x + 2500)} + \frac{1}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{x*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}} - \frac{40(\frac{\frac{-1}{2}(2x - 80 + 0)}{(x^{2} - 80x + 2500)^{\frac{3}{2}}})}{sqrt(x^{2} + 80x + 2500)} - \frac{40*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(2x + 80 + 0)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}})xsqrt(x^{2} - 80x + 2500) - \frac{sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{x(2x - 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} - 40(\frac{\frac{-3}{2}(2x + 80 + 0)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}})sqrt(x^{2} - 80x + 2500) - \frac{40(2x - 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}}\\=&\frac{-x^{2}}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{80x}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{1}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{2x^{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} - \frac{40x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{1600}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{40x}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} + \frac{1600}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)^{\frac{3}{2}}} + \frac{3x^{2}sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} + \frac{240xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} - \frac{sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} + \frac{4800sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} + \frac{1600}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{sqrt({(40 - x)}^{2} + {30}^{2})}{sqrt({(40 + x)}^{2} + {30}^{2})} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sqrt(x^{2} - 80x + 2500)}{sqrt(x^{2} + 80x + 2500)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{sqrt(x^{2} - 80x + 2500)}{sqrt(x^{2} + 80x + 2500)}\right)}{dx}\\=&\frac{(2x - 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{sqrt(x^{2} - 80x + 2500)*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}}\\=&\frac{x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{40}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{40sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{40}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{40sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(2x - 80 + 0)}{(x^{2} - 80x + 2500)^{\frac{3}{2}}})x}{sqrt(x^{2} + 80x + 2500)} + \frac{1}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{x*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}} - \frac{40(\frac{\frac{-1}{2}(2x - 80 + 0)}{(x^{2} - 80x + 2500)^{\frac{3}{2}}})}{sqrt(x^{2} + 80x + 2500)} - \frac{40*-(2x + 80 + 0)*\frac{1}{2}}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)(x^{2} + 80x + 2500)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(2x + 80 + 0)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}})xsqrt(x^{2} - 80x + 2500) - \frac{sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{x(2x - 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} - 40(\frac{\frac{-3}{2}(2x + 80 + 0)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}})sqrt(x^{2} - 80x + 2500) - \frac{40(2x - 80 + 0)*\frac{1}{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}}\\=&\frac{-x^{2}}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{80x}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{1}{(x^{2} - 80x + 2500)^{\frac{1}{2}}sqrt(x^{2} + 80x + 2500)} - \frac{2x^{2}}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} - \frac{40x}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)^{\frac{3}{2}}} - \frac{1600}{(x^{2} - 80x + 2500)^{\frac{3}{2}}sqrt(x^{2} + 80x + 2500)} + \frac{40x}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}} + \frac{1600}{(x^{2} - 80x + 2500)^{\frac{1}{2}}(x^{2} + 80x + 2500)^{\frac{3}{2}}} + \frac{3x^{2}sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} + \frac{240xsqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} - \frac{sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{3}{2}}} + \frac{4800sqrt(x^{2} - 80x + 2500)}{(x^{2} + 80x + 2500)^{\frac{5}{2}}} + \frac{1600}{(x^{2} + 80x + 2500)^{\frac{3}{2}}(x^{2} - 80x + 2500)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
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