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 D 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{D}^{e^{D}} 关于 D 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{D}^{e^{D}}\right)}{dD}\\=&(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})\\=&\frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\right)}{dD}\\=&\frac{-1}{ln^{2}(D)(D)} - \frac{-log_{D}^{e^{D}}}{D^{2}ln(D)} - \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{Dln(D)} - \frac{log_{D}^{e^{D}}*-1}{Dln^{2}(D)(D)}\\=&\frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\right)}{dD}\\=&\frac{-2*-1}{D^{2}ln^{2}(D)} - \frac{2*-2}{Dln^{3}(D)(D)} + \frac{-2log_{D}^{e^{D}}}{D^{3}ln(D)} + \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln(D)} + \frac{log_{D}^{e^{D}}*-1}{D^{2}ln^{2}(D)(D)} + \frac{2*-2log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} + \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln^{2}(D)} + \frac{2log_{D}^{e^{D}}*-2}{D^{2}ln^{3}(D)(D)}\\=&\frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\right)}{dD}\\=&\frac{3*-2}{D^{3}ln^{2}(D)} + \frac{3*-2}{D^{2}ln^{3}(D)(D)} + \frac{6*-2}{D^{3}ln^{3}(D)} + \frac{6*-3}{D^{2}ln^{4}(D)(D)} - \frac{2*-3log_{D}^{e^{D}}}{D^{4}ln(D)} - \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln(D)} - \frac{2log_{D}^{e^{D}}*-1}{D^{3}ln^{2}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}*-2}{D^{3}ln^{3}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{3}(D)} - \frac{6log_{D}^{e^{D}}*-3}{D^{3}ln^{4}(D)(D)}\\=&\frac{-8}{D^{3}ln^{2}(D)} - \frac{24}{D^{3}ln^{3}(D)} - \frac{24}{D^{3}ln^{4}(D)} + \frac{6log_{D}^{e^{D}}}{D^{4}ln(D)} + \frac{22log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} + \frac{36log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} + \frac{24log_{D}^{e^{D}}}{D^{4}ln^{4}(D)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{D}^{e^{D}} 关于 D 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{D}^{e^{D}}\right)}{dD}\\=&(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})\\=&\frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\right)}{dD}\\=&\frac{-1}{ln^{2}(D)(D)} - \frac{-log_{D}^{e^{D}}}{D^{2}ln(D)} - \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{Dln(D)} - \frac{log_{D}^{e^{D}}*-1}{Dln^{2}(D)(D)}\\=&\frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\right)}{dD}\\=&\frac{-2*-1}{D^{2}ln^{2}(D)} - \frac{2*-2}{Dln^{3}(D)(D)} + \frac{-2log_{D}^{e^{D}}}{D^{3}ln(D)} + \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln(D)} + \frac{log_{D}^{e^{D}}*-1}{D^{2}ln^{2}(D)(D)} + \frac{2*-2log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} + \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln^{2}(D)} + \frac{2log_{D}^{e^{D}}*-2}{D^{2}ln^{3}(D)(D)}\\=&\frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\right)}{dD}\\=&\frac{3*-2}{D^{3}ln^{2}(D)} + \frac{3*-2}{D^{2}ln^{3}(D)(D)} + \frac{6*-2}{D^{3}ln^{3}(D)} + \frac{6*-3}{D^{2}ln^{4}(D)(D)} - \frac{2*-3log_{D}^{e^{D}}}{D^{4}ln(D)} - \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln(D)} - \frac{2log_{D}^{e^{D}}*-1}{D^{3}ln^{2}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}*-2}{D^{3}ln^{3}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{3}(D)} - \frac{6log_{D}^{e^{D}}*-3}{D^{3}ln^{4}(D)(D)}\\=&\frac{-8}{D^{3}ln^{2}(D)} - \frac{24}{D^{3}ln^{3}(D)} - \frac{24}{D^{3}ln^{4}(D)} + \frac{6log_{D}^{e^{D}}}{D^{4}ln(D)} + \frac{22log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} + \frac{36log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} + \frac{24log_{D}^{e^{D}}}{D^{4}ln^{4}(D)}\\ \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。