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。
\[ \begin{equation}\begin{split}【1/1】求函数e^{e^{lg(x)}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{e^{lg(x)}}\right)}{dx}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{ln{10}(x)}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\right)}{dx}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{xln^{2}{10}}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{--2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{2}ln^{2}{10}} + \frac{-2e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{2}ln^{3}{10}} + \frac{-2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{2}ln^{3}{10}}\\=&\frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{2*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{3}ln^{2}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{3}ln^{3}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{3}ln^{3}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{3}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*3e^{{lg(x)}*{2}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}*-3*0}{x^{3}ln^{4}{10}} + \frac{2*-3e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} + \frac{2*2e^{lg(x)}e^{lg(x)}e^{e^{lg(x)}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-3*0}{x^{3}ln^{4}{10}}\\=&\frac{-6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{11e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} + \frac{11e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} - \frac{12e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{4}}}{x^{4}ln^{4}{10}} + \frac{5e^{{lg(x)}*{3}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{6e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{e^{lg(x)}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{e^{lg(x)}}\right)}{dx}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{ln{10}(x)}\\=&\frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}}\right)}{dx}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{xln{10}(x)ln{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{xln^{2}{10}}\\=&\frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{2}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{--2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln{10}} - \frac{e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{2}ln^{2}{10}} + \frac{-2e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{2}ln^{3}{10}} + \frac{-2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{2}ln{10}(x)ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{2}ln^{3}{10}}\\=&\frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{2}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{3}ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{3}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{2*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln{10}} + \frac{2e^{e^{lg(x)}}e^{lg(x)}*-0}{x^{3}ln^{2}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-2*0}{x^{3}ln^{3}{10}} - \frac{3*-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{2}{10}} - \frac{3e^{e^{lg(x)}}e^{lg(x)}*-2*0}{x^{3}ln^{3}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{3}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*3e^{{lg(x)}*{2}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}*-3*0}{x^{3}ln^{4}{10}} + \frac{2*-3e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} + \frac{2*2e^{lg(x)}e^{lg(x)}e^{e^{lg(x)}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{2e^{{lg(x)}*{2}}e^{e^{lg(x)}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{{lg(x)}*{2}}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}*2e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}*-3*0}{x^{3}ln^{4}{10}} + \frac{-3e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{3}ln{10}(x)ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}*-3*0}{x^{3}ln^{4}{10}}\\=&\frac{-6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln{10}} + \frac{11e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{2}{10}} + \frac{11e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{2}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{3}{10}} - \frac{12e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{3}{10}} - \frac{6e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{3}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{4}}}{x^{4}ln^{4}{10}} + \frac{5e^{{lg(x)}*{3}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{6e^{{lg(x)}*{2}}e^{e^{lg(x)}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{3}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{{lg(x)}*{2}}}{x^{4}ln^{4}{10}} + \frac{e^{e^{lg(x)}}e^{lg(x)}}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
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