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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{x - 1}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{x - 1}^{x}\right)}{dx}\\=&(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})\\=&\frac{1}{xln(x - 1)} - \frac{log_{x - 1}^{x}}{(x - 1)ln(x - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln(x - 1)} - \frac{log_{x - 1}^{x}}{(x - 1)ln(x - 1)}\right)}{dx}\\=&\frac{-1}{x^{2}ln(x - 1)} + \frac{-(1 + 0)}{xln^{2}(x - 1)(x - 1)} - \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})log_{x - 1}^{x}}{ln(x - 1)} - \frac{(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)ln(x - 1)} - \frac{log_{x - 1}^{x}*-(1 + 0)}{(x - 1)ln^{2}(x - 1)(x - 1)}\\=&\frac{-1}{x^{2}ln(x - 1)} - \frac{2}{(x - 1)xln^{2}(x - 1)} + \frac{log_{x - 1}^{x}}{(x - 1)^{2}ln(x - 1)} + \frac{2log_{x - 1}^{x}}{(x - 1)^{2}ln^{2}(x - 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln(x - 1)} - \frac{2}{(x - 1)xln^{2}(x - 1)} + \frac{log_{x - 1}^{x}}{(x - 1)^{2}ln(x - 1)} + \frac{2log_{x - 1}^{x}}{(x - 1)^{2}ln^{2}(x - 1)}\right)}{dx}\\=&\frac{--2}{x^{3}ln(x - 1)} - \frac{-(1 + 0)}{x^{2}ln^{2}(x - 1)(x - 1)} - \frac{2(\frac{-(1 + 0)}{(x - 1)^{2}})}{xln^{2}(x - 1)} - \frac{2*-1}{(x - 1)x^{2}ln^{2}(x - 1)} - \frac{2*-2(1 + 0)}{(x - 1)xln^{3}(x - 1)(x - 1)} + \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})log_{x - 1}^{x}}{ln(x - 1)} + \frac{(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)^{2}ln(x - 1)} + \frac{log_{x - 1}^{x}*-(1 + 0)}{(x - 1)^{2}ln^{2}(x - 1)(x - 1)} + \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})log_{x - 1}^{x}}{ln^{2}(x - 1)} + \frac{2(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)^{2}ln^{2}(x - 1)} + \frac{2log_{x - 1}^{x}*-2(1 + 0)}{(x - 1)^{2}ln^{3}(x - 1)(x - 1)}\\=&\frac{2}{x^{3}ln(x - 1)} + \frac{3}{(x - 1)x^{2}ln^{2}(x - 1)} + \frac{3}{(x - 1)^{2}xln^{2}(x - 1)} + \frac{6}{(x - 1)^{2}xln^{3}(x - 1)} - \frac{2log_{x - 1}^{x}}{(x - 1)^{3}ln(x - 1)} - \frac{6log_{x - 1}^{x}}{(x - 1)^{3}ln^{2}(x - 1)} - \frac{6log_{x - 1}^{x}}{(x - 1)^{3}ln^{3}(x - 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln(x - 1)} + \frac{3}{(x - 1)x^{2}ln^{2}(x - 1)} + \frac{3}{(x - 1)^{2}xln^{2}(x - 1)} + \frac{6}{(x - 1)^{2}xln^{3}(x - 1)} - \frac{2log_{x - 1}^{x}}{(x - 1)^{3}ln(x - 1)} - \frac{6log_{x - 1}^{x}}{(x - 1)^{3}ln^{2}(x - 1)} - \frac{6log_{x - 1}^{x}}{(x - 1)^{3}ln^{3}(x - 1)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln(x - 1)} + \frac{2*-(1 + 0)}{x^{3}ln^{2}(x - 1)(x - 1)} + \frac{3(\frac{-(1 + 0)}{(x - 1)^{2}})}{x^{2}ln^{2}(x - 1)} + \frac{3*-2}{(x - 1)x^{3}ln^{2}(x - 1)} + \frac{3*-2(1 + 0)}{(x - 1)x^{2}ln^{3}(x - 1)(x - 1)} + \frac{3(\frac{-2(1 + 0)}{(x - 1)^{3}})}{xln^{2}(x - 1)} + \frac{3*-1}{(x - 1)^{2}x^{2}ln^{2}(x - 1)} + \frac{3*-2(1 + 0)}{(x - 1)^{2}xln^{3}(x - 1)(x - 1)} + \frac{6(\frac{-2(1 + 0)}{(x - 1)^{3}})}{xln^{3}(x - 1)} + \frac{6*-1}{(x - 1)^{2}x^{2}ln^{3}(x - 1)} + \frac{6*-3(1 + 0)}{(x - 1)^{2}xln^{4}(x - 1)(x - 1)} - \frac{2(\frac{-3(1 + 0)}{(x - 1)^{4}})log_{x - 1}^{x}}{ln(x - 1)} - \frac{2(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)^{3}ln(x - 1)} - \frac{2log_{x - 1}^{x}*-(1 + 0)}{(x - 1)^{3}ln^{2}(x - 1)(x - 1)} - \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})log_{x - 1}^{x}}{ln^{2}(x - 1)} - \frac{6(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)^{3}ln^{2}(x - 1)} - \frac{6log_{x - 1}^{x}*-2(1 + 0)}{(x - 1)^{3}ln^{3}(x - 1)(x - 1)} - \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})log_{x - 1}^{x}}{ln^{3}(x - 1)} - \frac{6(\frac{(\frac{(1)}{(x)} - \frac{(1 + 0)log_{x - 1}^{x}}{(x - 1)})}{(ln(x - 1))})}{(x - 1)^{3}ln^{3}(x - 1)} - \frac{6log_{x - 1}^{x}*-3(1 + 0)}{(x - 1)^{3}ln^{4}(x - 1)(x - 1)}\\=&\frac{-6}{x^{4}ln(x - 1)} - \frac{8}{(x - 1)x^{3}ln^{2}(x - 1)} - \frac{6}{(x - 1)^{2}x^{2}ln^{2}(x - 1)} - \frac{12}{(x - 1)^{2}x^{2}ln^{3}(x - 1)} - \frac{8}{(x - 1)^{3}xln^{2}(x - 1)} - \frac{24}{(x - 1)^{3}xln^{3}(x - 1)} - \frac{24}{(x - 1)^{3}xln^{4}(x - 1)} + \frac{6log_{x - 1}^{x}}{(x - 1)^{4}ln(x - 1)} + \frac{22log_{x - 1}^{x}}{(x - 1)^{4}ln^{2}(x - 1)} + \frac{36log_{x - 1}^{x}}{(x - 1)^{4}ln^{3}(x - 1)} + \frac{24log_{x - 1}^{x}}{(x - 1)^{4}ln^{4}(x - 1)}\\ \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！
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。