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 k 求 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{({k}^{2} - 2rkm - (1 - r)k + r{m}^{2})} + \frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{(m(m - 1)(1 - r))}) 关于 k 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2rk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(m^{2} - rm^{2} - m + rm)} + \frac{k^{2}}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(m^{2} - rm^{2} - m + rm)} + \frac{2rk}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(m^{2} - rm^{2} - m + rm)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2rk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(m^{2} - rm^{2} - m + rm)} + \frac{k^{2}}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(m^{2} - rm^{2} - m + rm)} + \frac{2rk}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(m^{2} - rm^{2} - m + rm)}\right)}{dk}\\=&(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})k^{2} + \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rmk - \frac{2rm}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})k - \frac{2}{(k^{2} - 2rmk - k + rk + rm^{2})} + 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rk + \frac{2r}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rmk - \frac{2rm}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})k^{2} + \frac{2k}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rm^{2} + 0 - 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})k - \frac{2}{(m^{2} - rm^{2} - m + rm)} + 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rk + \frac{2r}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rm^{2} + 0\\=&\frac{-2k^{3}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{6rmk^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{5rk^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{5k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{4r^{2}m^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{6r^{2}mk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{6rmk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{4rk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm}{(m^{2} - rm^{2} - m + rm)} - \frac{2r^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2r^{2}m^{3}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2k}{(m^{2} - rm^{2} - m + rm)} - \frac{r^{2}m^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2r}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2r}{(m^{2} - rm^{2} - m + rm)} - \frac{2}{(m^{2} - rm^{2} - m + rm)} - \frac{2}{(k^{2} - 2rmk - k + rk + rm^{2})}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{({k}^{2} - 2rkm - (1 - r)k + r{m}^{2})} + \frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{(m(m - 1)(1 - r))}) 关于 k 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2rk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(m^{2} - rm^{2} - m + rm)} + \frac{k^{2}}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(m^{2} - rm^{2} - m + rm)} + \frac{2rk}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(m^{2} - rm^{2} - m + rm)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2rk}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2rmk}{(m^{2} - rm^{2} - m + rm)} + \frac{k^{2}}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{2k}{(m^{2} - rm^{2} - m + rm)} + \frac{2rk}{(m^{2} - rm^{2} - m + rm)} + \frac{rm^{2}}{(m^{2} - rm^{2} - m + rm)}\right)}{dk}\\=&(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})k^{2} + \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rmk - \frac{2rm}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})k - \frac{2}{(k^{2} - 2rmk - k + rk + rm^{2})} + 2(\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rk + \frac{2r}{(k^{2} - 2rmk - k + rk + rm^{2})} - 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rmk - \frac{2rm}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})k^{2} + \frac{2k}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(2k - 2rm - 1 + r + 0)}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}})rm^{2} + 0 - 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})k - \frac{2}{(m^{2} - rm^{2} - m + rm)} + 2(\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rk + \frac{2r}{(m^{2} - rm^{2} - m + rm)} + (\frac{-(0 + 0 + 0 + 0)}{(m^{2} - rm^{2} - m + rm)^{2}})rm^{2} + 0\\=&\frac{-2k^{3}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{6rmk^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{5rk^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{5k^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})} - \frac{4r^{2}m^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{6r^{2}mk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{6rmk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{4rk}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm}{(m^{2} - rm^{2} - m + rm)} - \frac{2r^{2}k}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} - \frac{2rm}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2r^{2}m^{3}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2k}{(m^{2} - rm^{2} - m + rm)} - \frac{r^{2}m^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{rm^{2}}{(k^{2} - 2rmk - k + rk + rm^{2})^{2}} + \frac{2r}{(k^{2} - 2rmk - k + rk + rm^{2})} + \frac{2r}{(m^{2} - rm^{2} - m + rm)} - \frac{2}{(m^{2} - rm^{2} - m + rm)} - \frac{2}{(k^{2} - 2rmk - k + rk + rm^{2})}\\ \end{split}\end{equation} \]
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