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 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(\frac{(x - 2)(x - 3)}{(x - 4)(x - 5)}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\right)}{dx}\\=&\frac{(\frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 5)} + \frac{(\frac{-(1 + 0)}{(x - 5)^{2}})x^{2}}{(x - 4)} + \frac{2x}{(x - 4)(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 5)^{2}})x}{(x - 4)} - \frac{5}{(x - 4)(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 5)^{2}})}{(x - 4)})*\frac{1}{2}}{(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\=&\frac{-x^{2}}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{x^{2}}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{x}{(x - 4)(x - 5)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{5}{2(x - 5)(x - 4)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(\frac{(x - 2)(x - 3)}{(x - 4)(x - 5)}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\right)}{dx}\\=&\frac{(\frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 5)} + \frac{(\frac{-(1 + 0)}{(x - 5)^{2}})x^{2}}{(x - 4)} + \frac{2x}{(x - 4)(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 5)^{2}})x}{(x - 4)} - \frac{5}{(x - 4)(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 5)^{2}})}{(x - 4)})*\frac{1}{2}}{(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\=&\frac{-x^{2}}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{x^{2}}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{x}{(x - 4)(x - 5)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{5}{2(x - 5)(x - 4)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
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。