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 m 求 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{({k}^{2} - 2rkm - (1 - r)k + r{m}^{2})} + r + \frac{(1 - r)k(k - rm - 2(1 - r))}{(k - rm)(k - rm - (1 - r))} - rm 关于 m 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{2krm}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2k}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{k^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{rm^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} - rm - \frac{krm}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}m}{(k - rm)(k - rm + r - 1)} + \frac{4kr}{(k - rm)(k - rm + r - 1)} - \frac{k^{2}r}{(k - rm)(k - rm + r - 1)} - \frac{2kr^{2}}{(k - rm)(k - rm + r - 1)} - \frac{2k}{(k - rm)(k - rm + r - 1)} + \frac{k^{2}}{(k - rm)(k - rm + r - 1)} + r\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{2krm}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2k}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{k^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{rm^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} - rm - \frac{krm}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}m}{(k - rm)(k - rm + r - 1)} + \frac{4kr}{(k - rm)(k - rm + r - 1)} - \frac{k^{2}r}{(k - rm)(k - rm + r - 1)} - \frac{2kr^{2}}{(k - rm)(k - rm + r - 1)} - \frac{2k}{(k - rm)(k - rm + r - 1)} + \frac{k^{2}}{(k - rm)(k - rm + r - 1)} + r\right)}{dm}\\=& - 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})krm - \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} + 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})kr + 0 - 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})k + 0 + (\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})k^{2} + 0 + (\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})rm^{2} + \frac{r*2m}{(-2krm + kr - k + k^{2} + rm^{2})} - r - \frac{(\frac{-(0 - r)}{(k - rm)^{2}})krm}{(k - rm + r - 1)} - \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})krm}{(k - rm)} - \frac{kr}{(k - rm)(k - rm + r - 1)} + \frac{(\frac{-(0 - r)}{(k - rm)^{2}})kr^{2}m}{(k - rm + r - 1)} + \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr^{2}m}{(k - rm)} + \frac{kr^{2}}{(k - rm)(k - rm + r - 1)} + \frac{4(\frac{-(0 - r)}{(k - rm)^{2}})kr}{(k - rm + r - 1)} + \frac{4(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr}{(k - rm)} + 0 - \frac{(\frac{-(0 - r)}{(k - rm)^{2}})k^{2}r}{(k - rm + r - 1)} - \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k^{2}r}{(k - rm)} + 0 - \frac{2(\frac{-(0 - r)}{(k - rm)^{2}})kr^{2}}{(k - rm + r - 1)} - \frac{2(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr^{2}}{(k - rm)} + 0 - \frac{2(\frac{-(0 - r)}{(k - rm)^{2}})k}{(k - rm + r - 1)} - \frac{2(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k}{(k - rm)} + 0 + \frac{(\frac{-(0 - r)}{(k - rm)^{2}})k^{2}}{(k - rm + r - 1)} + \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k^{2}}{(k - rm)} + 0 + 0\\=&\frac{-4k^{2}r^{2}m}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{6kr^{2}m^{2}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{4kr^{2}m}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{4krm}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{2k^{2}rm}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{4k^{2}r}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{4k^{2}r^{2}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{2k^{3}r}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2r^{2}m^{3}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{2rm}{(-2krm + kr - k + k^{2} + rm^{2})} - r - \frac{kr^{2}m}{(k - rm)^{2}(k - rm + r - 1)} - \frac{kr^{2}m}{(k - rm + r - 1)^{2}(k - rm)} + \frac{kr^{3}m}{(k - rm)^{2}(k - rm + r - 1)} + \frac{kr^{3}m}{(k - rm + r - 1)^{2}(k - rm)} - \frac{kr}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}}{(k - rm)(k - rm + r - 1)} + \frac{4kr^{2}}{(k - rm)^{2}(k - rm + r - 1)} + \frac{4kr^{2}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{k^{2}r^{2}}{(k - rm)^{2}(k - rm + r - 1)} - \frac{k^{2}r^{2}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{2kr^{3}}{(k - rm)^{2}(k - rm + r - 1)} - \frac{2kr^{3}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{2kr}{(k - rm)^{2}(k - rm + r - 1)} - \frac{2kr}{(k - rm + r - 1)^{2}(k - rm)} + \frac{k^{2}r}{(k - rm)^{2}(k - rm + r - 1)} + \frac{k^{2}r}{(k - rm + r - 1)^{2}(k - rm)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{({k}^{2} - 2rkm - 2(1 - r)k + r{m}^{2})}{({k}^{2} - 2rkm - (1 - r)k + r{m}^{2})} + r + \frac{(1 - r)k(k - rm - 2(1 - r))}{(k - rm)(k - rm - (1 - r))} - rm 关于 m 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{2krm}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2k}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{k^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{rm^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} - rm - \frac{krm}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}m}{(k - rm)(k - rm + r - 1)} + \frac{4kr}{(k - rm)(k - rm + r - 1)} - \frac{k^{2}r}{(k - rm)(k - rm + r - 1)} - \frac{2kr^{2}}{(k - rm)(k - rm + r - 1)} - \frac{2k}{(k - rm)(k - rm + r - 1)} + \frac{k^{2}}{(k - rm)(k - rm + r - 1)} + r\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{2krm}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2k}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{k^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} + \frac{rm^{2}}{(-2krm + kr - k + k^{2} + rm^{2})} - rm - \frac{krm}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}m}{(k - rm)(k - rm + r - 1)} + \frac{4kr}{(k - rm)(k - rm + r - 1)} - \frac{k^{2}r}{(k - rm)(k - rm + r - 1)} - \frac{2kr^{2}}{(k - rm)(k - rm + r - 1)} - \frac{2k}{(k - rm)(k - rm + r - 1)} + \frac{k^{2}}{(k - rm)(k - rm + r - 1)} + r\right)}{dm}\\=& - 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})krm - \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} + 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})kr + 0 - 2(\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})k + 0 + (\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})k^{2} + 0 + (\frac{-(-2kr + 0 + 0 + 0 + r*2m)}{(-2krm + kr - k + k^{2} + rm^{2})^{2}})rm^{2} + \frac{r*2m}{(-2krm + kr - k + k^{2} + rm^{2})} - r - \frac{(\frac{-(0 - r)}{(k - rm)^{2}})krm}{(k - rm + r - 1)} - \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})krm}{(k - rm)} - \frac{kr}{(k - rm)(k - rm + r - 1)} + \frac{(\frac{-(0 - r)}{(k - rm)^{2}})kr^{2}m}{(k - rm + r - 1)} + \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr^{2}m}{(k - rm)} + \frac{kr^{2}}{(k - rm)(k - rm + r - 1)} + \frac{4(\frac{-(0 - r)}{(k - rm)^{2}})kr}{(k - rm + r - 1)} + \frac{4(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr}{(k - rm)} + 0 - \frac{(\frac{-(0 - r)}{(k - rm)^{2}})k^{2}r}{(k - rm + r - 1)} - \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k^{2}r}{(k - rm)} + 0 - \frac{2(\frac{-(0 - r)}{(k - rm)^{2}})kr^{2}}{(k - rm + r - 1)} - \frac{2(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})kr^{2}}{(k - rm)} + 0 - \frac{2(\frac{-(0 - r)}{(k - rm)^{2}})k}{(k - rm + r - 1)} - \frac{2(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k}{(k - rm)} + 0 + \frac{(\frac{-(0 - r)}{(k - rm)^{2}})k^{2}}{(k - rm + r - 1)} + \frac{(\frac{-(0 - r + 0 + 0)}{(k - rm + r - 1)^{2}})k^{2}}{(k - rm)} + 0 + 0\\=&\frac{-4k^{2}r^{2}m}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{6kr^{2}m^{2}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{4kr^{2}m}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{4krm}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{2k^{2}rm}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{4k^{2}r}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{4k^{2}r^{2}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{2k^{3}r}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} - \frac{2kr}{(-2krm + kr - k + k^{2} + rm^{2})} - \frac{2r^{2}m^{3}}{(-2krm + kr - k + k^{2} + rm^{2})^{2}} + \frac{2rm}{(-2krm + kr - k + k^{2} + rm^{2})} - r - \frac{kr^{2}m}{(k - rm)^{2}(k - rm + r - 1)} - \frac{kr^{2}m}{(k - rm + r - 1)^{2}(k - rm)} + \frac{kr^{3}m}{(k - rm)^{2}(k - rm + r - 1)} + \frac{kr^{3}m}{(k - rm + r - 1)^{2}(k - rm)} - \frac{kr}{(k - rm)(k - rm + r - 1)} + \frac{kr^{2}}{(k - rm)(k - rm + r - 1)} + \frac{4kr^{2}}{(k - rm)^{2}(k - rm + r - 1)} + \frac{4kr^{2}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{k^{2}r^{2}}{(k - rm)^{2}(k - rm + r - 1)} - \frac{k^{2}r^{2}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{2kr^{3}}{(k - rm)^{2}(k - rm + r - 1)} - \frac{2kr^{3}}{(k - rm + r - 1)^{2}(k - rm)} - \frac{2kr}{(k - rm)^{2}(k - rm + r - 1)} - \frac{2kr}{(k - rm + r - 1)^{2}(k - rm)} + \frac{k^{2}r}{(k - rm)^{2}(k - rm + r - 1)} + \frac{k^{2}r}{(k - rm + r - 1)^{2}(k - rm)}\\ \end{split}\end{equation} \]
你的问题在这里没有得到解决？请到 热门难题 里面看看吧！
最 新 发 布
新增加身体健康评估计算器，位置：“数学运算 > 身体健康评估”。
新增加学习笔记(安卓版)百度网盘快速下载应用程序，欢迎使用。
新增加学习笔记(安卓版)本站下载应用程序，欢迎使用。
新增线性代数行列式的计算，欢迎使用。
数学计算和一元方程已经支持正割函数和余割函数，欢迎使用。
新增加贷款计算器模块（具体位置：数学运算 > 贷款计算器），欢迎使用。