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 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(xlg(x) - 2x + 1)}{(x - 1)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{xlg(x)}{(x - 1)} - \frac{2x}{(x - 1)} + \frac{1}{(x - 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{xlg(x)}{(x - 1)} - \frac{2x}{(x - 1)} + \frac{1}{(x - 1)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x - 1)^{2}})xlg(x) + \frac{lg(x)}{(x - 1)} + \frac{x}{(x - 1)ln{10}(x)} - 2(\frac{-(1 + 0)}{(x - 1)^{2}})x - \frac{2}{(x - 1)} + (\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{-xlg(x)}{(x - 1)^{2}} + \frac{lg(x)}{(x - 1)} + \frac{1}{(x - 1)ln{10}} + \frac{2x}{(x - 1)^{2}} - \frac{1}{(x - 1)^{2}} - \frac{2}{(x - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-xlg(x)}{(x - 1)^{2}} + \frac{lg(x)}{(x - 1)} + \frac{1}{(x - 1)ln{10}} + \frac{2x}{(x - 1)^{2}} - \frac{1}{(x - 1)^{2}} - \frac{2}{(x - 1)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 1)^{3}})xlg(x) - \frac{lg(x)}{(x - 1)^{2}} - \frac{x}{(x - 1)^{2}ln{10}(x)} + (\frac{-(1 + 0)}{(x - 1)^{2}})lg(x) + \frac{1}{(x - 1)ln{10}(x)} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{ln{10}} + \frac{-0}{(x - 1)ln^{2}{10}} + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})x + \frac{2}{(x - 1)^{2}} - (\frac{-2(1 + 0)}{(x - 1)^{3}}) - 2(\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{2xlg(x)}{(x - 1)^{3}} - \frac{2lg(x)}{(x - 1)^{2}} - \frac{2}{(x - 1)^{2}ln{10}} + \frac{1}{(x - 1)xln{10}} - \frac{4x}{(x - 1)^{3}} + \frac{4}{(x - 1)^{2}} + \frac{2}{(x - 1)^{3}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2xlg(x)}{(x - 1)^{3}} - \frac{2lg(x)}{(x - 1)^{2}} - \frac{2}{(x - 1)^{2}ln{10}} + \frac{1}{(x - 1)xln{10}} - \frac{4x}{(x - 1)^{3}} + \frac{4}{(x - 1)^{2}} + \frac{2}{(x - 1)^{3}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 1)^{4}})xlg(x) + \frac{2lg(x)}{(x - 1)^{3}} + \frac{2x}{(x - 1)^{3}ln{10}(x)} - 2(\frac{-2(1 + 0)}{(x - 1)^{3}})lg(x) - \frac{2}{(x - 1)^{2}ln{10}(x)} - \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{ln{10}} - \frac{2*-0}{(x - 1)^{2}ln^{2}{10}} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{xln{10}} + \frac{-1}{(x - 1)x^{2}ln{10}} + \frac{-0}{(x - 1)xln^{2}{10}} - 4(\frac{-3(1 + 0)}{(x - 1)^{4}})x - \frac{4}{(x - 1)^{3}} + 4(\frac{-2(1 + 0)}{(x - 1)^{3}}) + 2(\frac{-3(1 + 0)}{(x - 1)^{4}})\\=&\frac{-6xlg(x)}{(x - 1)^{4}} + \frac{6lg(x)}{(x - 1)^{3}} + \frac{6}{(x - 1)^{3}ln{10}} - \frac{3}{(x - 1)^{2}xln{10}} - \frac{1}{(x - 1)x^{2}ln{10}} + \frac{12x}{(x - 1)^{4}} - \frac{12}{(x - 1)^{3}} - \frac{6}{(x - 1)^{4}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6xlg(x)}{(x - 1)^{4}} + \frac{6lg(x)}{(x - 1)^{3}} + \frac{6}{(x - 1)^{3}ln{10}} - \frac{3}{(x - 1)^{2}xln{10}} - \frac{1}{(x - 1)x^{2}ln{10}} + \frac{12x}{(x - 1)^{4}} - \frac{12}{(x - 1)^{3}} - \frac{6}{(x - 1)^{4}}\right)}{dx}\\=&-6(\frac{-4(1 + 0)}{(x - 1)^{5}})xlg(x) - \frac{6lg(x)}{(x - 1)^{4}} - \frac{6x}{(x - 1)^{4}ln{10}(x)} + 6(\frac{-3(1 + 0)}{(x - 1)^{4}})lg(x) + \frac{6}{(x - 1)^{3}ln{10}(x)} + \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})}{ln{10}} + \frac{6*-0}{(x - 1)^{3}ln^{2}{10}} - \frac{3(\frac{-2(1 + 0)}{(x - 1)^{3}})}{xln{10}} - \frac{3*-1}{(x - 1)^{2}x^{2}ln{10}} - \frac{3*-0}{(x - 1)^{2}xln^{2}{10}} - \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{x^{2}ln{10}} - \frac{-2}{(x - 1)x^{3}ln{10}} - \frac{-0}{(x - 1)x^{2}ln^{2}{10}} + 12(\frac{-4(1 + 0)}{(x - 1)^{5}})x + \frac{12}{(x - 1)^{4}} - 12(\frac{-3(1 + 0)}{(x - 1)^{4}}) - 6(\frac{-4(1 + 0)}{(x - 1)^{5}})\\=&\frac{24xlg(x)}{(x - 1)^{5}} - \frac{24lg(x)}{(x - 1)^{4}} - \frac{24}{(x - 1)^{4}ln{10}} + \frac{12}{(x - 1)^{3}xln{10}} + \frac{4}{(x - 1)^{2}x^{2}ln{10}} + \frac{2}{(x - 1)x^{3}ln{10}} - \frac{48x}{(x - 1)^{5}} + \frac{48}{(x - 1)^{4}} + \frac{24}{(x - 1)^{5}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(xlg(x) - 2x + 1)}{(x - 1)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{xlg(x)}{(x - 1)} - \frac{2x}{(x - 1)} + \frac{1}{(x - 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{xlg(x)}{(x - 1)} - \frac{2x}{(x - 1)} + \frac{1}{(x - 1)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x - 1)^{2}})xlg(x) + \frac{lg(x)}{(x - 1)} + \frac{x}{(x - 1)ln{10}(x)} - 2(\frac{-(1 + 0)}{(x - 1)^{2}})x - \frac{2}{(x - 1)} + (\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{-xlg(x)}{(x - 1)^{2}} + \frac{lg(x)}{(x - 1)} + \frac{1}{(x - 1)ln{10}} + \frac{2x}{(x - 1)^{2}} - \frac{1}{(x - 1)^{2}} - \frac{2}{(x - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-xlg(x)}{(x - 1)^{2}} + \frac{lg(x)}{(x - 1)} + \frac{1}{(x - 1)ln{10}} + \frac{2x}{(x - 1)^{2}} - \frac{1}{(x - 1)^{2}} - \frac{2}{(x - 1)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 1)^{3}})xlg(x) - \frac{lg(x)}{(x - 1)^{2}} - \frac{x}{(x - 1)^{2}ln{10}(x)} + (\frac{-(1 + 0)}{(x - 1)^{2}})lg(x) + \frac{1}{(x - 1)ln{10}(x)} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{ln{10}} + \frac{-0}{(x - 1)ln^{2}{10}} + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})x + \frac{2}{(x - 1)^{2}} - (\frac{-2(1 + 0)}{(x - 1)^{3}}) - 2(\frac{-(1 + 0)}{(x - 1)^{2}})\\=&\frac{2xlg(x)}{(x - 1)^{3}} - \frac{2lg(x)}{(x - 1)^{2}} - \frac{2}{(x - 1)^{2}ln{10}} + \frac{1}{(x - 1)xln{10}} - \frac{4x}{(x - 1)^{3}} + \frac{4}{(x - 1)^{2}} + \frac{2}{(x - 1)^{3}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2xlg(x)}{(x - 1)^{3}} - \frac{2lg(x)}{(x - 1)^{2}} - \frac{2}{(x - 1)^{2}ln{10}} + \frac{1}{(x - 1)xln{10}} - \frac{4x}{(x - 1)^{3}} + \frac{4}{(x - 1)^{2}} + \frac{2}{(x - 1)^{3}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 1)^{4}})xlg(x) + \frac{2lg(x)}{(x - 1)^{3}} + \frac{2x}{(x - 1)^{3}ln{10}(x)} - 2(\frac{-2(1 + 0)}{(x - 1)^{3}})lg(x) - \frac{2}{(x - 1)^{2}ln{10}(x)} - \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{ln{10}} - \frac{2*-0}{(x - 1)^{2}ln^{2}{10}} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{xln{10}} + \frac{-1}{(x - 1)x^{2}ln{10}} + \frac{-0}{(x - 1)xln^{2}{10}} - 4(\frac{-3(1 + 0)}{(x - 1)^{4}})x - \frac{4}{(x - 1)^{3}} + 4(\frac{-2(1 + 0)}{(x - 1)^{3}}) + 2(\frac{-3(1 + 0)}{(x - 1)^{4}})\\=&\frac{-6xlg(x)}{(x - 1)^{4}} + \frac{6lg(x)}{(x - 1)^{3}} + \frac{6}{(x - 1)^{3}ln{10}} - \frac{3}{(x - 1)^{2}xln{10}} - \frac{1}{(x - 1)x^{2}ln{10}} + \frac{12x}{(x - 1)^{4}} - \frac{12}{(x - 1)^{3}} - \frac{6}{(x - 1)^{4}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6xlg(x)}{(x - 1)^{4}} + \frac{6lg(x)}{(x - 1)^{3}} + \frac{6}{(x - 1)^{3}ln{10}} - \frac{3}{(x - 1)^{2}xln{10}} - \frac{1}{(x - 1)x^{2}ln{10}} + \frac{12x}{(x - 1)^{4}} - \frac{12}{(x - 1)^{3}} - \frac{6}{(x - 1)^{4}}\right)}{dx}\\=&-6(\frac{-4(1 + 0)}{(x - 1)^{5}})xlg(x) - \frac{6lg(x)}{(x - 1)^{4}} - \frac{6x}{(x - 1)^{4}ln{10}(x)} + 6(\frac{-3(1 + 0)}{(x - 1)^{4}})lg(x) + \frac{6}{(x - 1)^{3}ln{10}(x)} + \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})}{ln{10}} + \frac{6*-0}{(x - 1)^{3}ln^{2}{10}} - \frac{3(\frac{-2(1 + 0)}{(x - 1)^{3}})}{xln{10}} - \frac{3*-1}{(x - 1)^{2}x^{2}ln{10}} - \frac{3*-0}{(x - 1)^{2}xln^{2}{10}} - \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{x^{2}ln{10}} - \frac{-2}{(x - 1)x^{3}ln{10}} - \frac{-0}{(x - 1)x^{2}ln^{2}{10}} + 12(\frac{-4(1 + 0)}{(x - 1)^{5}})x + \frac{12}{(x - 1)^{4}} - 12(\frac{-3(1 + 0)}{(x - 1)^{4}}) - 6(\frac{-4(1 + 0)}{(x - 1)^{5}})\\=&\frac{24xlg(x)}{(x - 1)^{5}} - \frac{24lg(x)}{(x - 1)^{4}} - \frac{24}{(x - 1)^{4}ln{10}} + \frac{12}{(x - 1)^{3}xln{10}} + \frac{4}{(x - 1)^{2}x^{2}ln{10}} + \frac{2}{(x - 1)x^{3}ln{10}} - \frac{48x}{(x - 1)^{5}} + \frac{48}{(x - 1)^{4}} + \frac{24}{(x - 1)^{5}}\\ \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。