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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{lg(lg(x))}{lg(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{lg(lg(x))}{lg(x)}\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)lg(x)} + \frac{lg(lg(x))*-1}{lg^{2}(x)ln{10}(x)}\\=&\frac{-lg(lg(x))}{xln{10}lg^{2}(x)} + \frac{1}{xln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-lg(lg(x))}{xln{10}lg^{2}(x)} + \frac{1}{xln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} - \frac{-0lg(lg(x))}{xln^{2}{10}lg^{2}(x)} - \frac{1}{xln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} - \frac{lg(lg(x))*-2}{xln{10}lg^{3}(x)ln{10}(x)} + \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{-2*0}{xln^{3}{10}lg^{2}(x)} + \frac{-2}{xln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} + \frac{2lg(lg(x))}{x^{2}ln^{2}{10}lg^{3}(x)} - \frac{3}{x^{2}ln^{3}{10}lg^{3}(x)} - \frac{1}{x^{2}ln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} + \frac{2lg(lg(x))}{x^{2}ln^{2}{10}lg^{3}(x)} - \frac{3}{x^{2}ln^{3}{10}lg^{3}(x)} - \frac{1}{x^{2}ln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} + \frac{-0lg(lg(x))}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{1}{x^{2}ln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} + \frac{lg(lg(x))*-2}{x^{2}ln{10}lg^{3}(x)ln{10}(x)} + \frac{2*-2lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} + \frac{2*-2*0lg(lg(x))}{x^{2}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{2}ln^{2}{10}ln{10}(lg(x))ln{10}(x)lg^{3}(x)} + \frac{2lg(lg(x))*-3}{x^{2}ln^{2}{10}lg^{4}(x)ln{10}(x)} - \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3*-3*0}{x^{2}ln^{4}{10}lg^{3}(x)} - \frac{3*-3}{x^{2}ln^{3}{10}lg^{4}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{3}{10}lg^{4}(x)} + \frac{11}{x^{3}ln^{4}{10}lg^{4}(x)} + \frac{9}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{3}ln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{3}{10}lg^{4}(x)} + \frac{11}{x^{3}ln^{4}{10}lg^{4}(x)} + \frac{9}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{3}ln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-2*-3lg(lg(x))}{x^{4}ln{10}lg^{2}(x)} - \frac{2*-0lg(lg(x))}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{2}{x^{3}ln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} - \frac{2lg(lg(x))*-2}{x^{3}ln{10}lg^{3}(x)ln{10}(x)} - \frac{6*-3lg(lg(x))}{x^{4}ln^{2}{10}lg^{3}(x)} - \frac{6*-2*0lg(lg(x))}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{6}{x^{3}ln^{2}{10}ln{10}(lg(x))ln{10}(x)lg^{3}(x)} - \frac{6lg(lg(x))*-3}{x^{3}ln^{2}{10}lg^{4}(x)ln{10}(x)} - \frac{6*-3lg(lg(x))}{x^{4}ln^{3}{10}lg^{4}(x)} - \frac{6*-3*0lg(lg(x))}{x^{3}ln^{4}{10}lg^{4}(x)} - \frac{6}{x^{3}ln^{3}{10}ln{10}(lg(x))ln{10}(x)lg^{4}(x)} - \frac{6lg(lg(x))*-4}{x^{3}ln^{3}{10}lg^{5}(x)ln{10}(x)} + \frac{11*-3}{x^{4}ln^{4}{10}lg^{4}(x)} + \frac{11*-4*0}{x^{3}ln^{5}{10}lg^{4}(x)} + \frac{11*-4}{x^{3}ln^{4}{10}lg^{5}(x)ln{10}(x)} + \frac{9*-3}{x^{4}ln^{3}{10}lg^{3}(x)} + \frac{9*-3*0}{x^{3}ln^{4}{10}lg^{3}(x)} + \frac{9*-3}{x^{3}ln^{3}{10}lg^{4}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{2}{10}lg^{2}(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2*-2}{x^{3}ln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{6lg(lg(x))}{x^{4}ln{10}lg^{2}(x)} + \frac{22lg(lg(x))}{x^{4}ln^{2}{10}lg^{3}(x)} + \frac{36lg(lg(x))}{x^{4}ln^{3}{10}lg^{4}(x)} + \frac{24lg(lg(x))}{x^{4}ln^{4}{10}lg^{5}(x)} - \frac{33}{x^{4}ln^{3}{10}lg^{3}(x)} - \frac{50}{x^{4}ln^{5}{10}lg^{5}(x)} - \frac{66}{x^{4}ln^{4}{10}lg^{4}(x)} - \frac{6}{x^{4}ln^{2}{10}lg^{2}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{lg(lg(x))}{lg(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{lg(lg(x))}{lg(x)}\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)lg(x)} + \frac{lg(lg(x))*-1}{lg^{2}(x)ln{10}(x)}\\=&\frac{-lg(lg(x))}{xln{10}lg^{2}(x)} + \frac{1}{xln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-lg(lg(x))}{xln{10}lg^{2}(x)} + \frac{1}{xln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} - \frac{-0lg(lg(x))}{xln^{2}{10}lg^{2}(x)} - \frac{1}{xln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} - \frac{lg(lg(x))*-2}{xln{10}lg^{3}(x)ln{10}(x)} + \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{-2*0}{xln^{3}{10}lg^{2}(x)} + \frac{-2}{xln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} + \frac{2lg(lg(x))}{x^{2}ln^{2}{10}lg^{3}(x)} - \frac{3}{x^{2}ln^{3}{10}lg^{3}(x)} - \frac{1}{x^{2}ln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{lg(lg(x))}{x^{2}ln{10}lg^{2}(x)} + \frac{2lg(lg(x))}{x^{2}ln^{2}{10}lg^{3}(x)} - \frac{3}{x^{2}ln^{3}{10}lg^{3}(x)} - \frac{1}{x^{2}ln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} + \frac{-0lg(lg(x))}{x^{2}ln^{2}{10}lg^{2}(x)} + \frac{1}{x^{2}ln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} + \frac{lg(lg(x))*-2}{x^{2}ln{10}lg^{3}(x)ln{10}(x)} + \frac{2*-2lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} + \frac{2*-2*0lg(lg(x))}{x^{2}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{2}ln^{2}{10}ln{10}(lg(x))ln{10}(x)lg^{3}(x)} + \frac{2lg(lg(x))*-3}{x^{2}ln^{2}{10}lg^{4}(x)ln{10}(x)} - \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{3*-3*0}{x^{2}ln^{4}{10}lg^{3}(x)} - \frac{3*-3}{x^{2}ln^{3}{10}lg^{4}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{3}{10}lg^{4}(x)} + \frac{11}{x^{3}ln^{4}{10}lg^{4}(x)} + \frac{9}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{3}ln^{2}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-2lg(lg(x))}{x^{3}ln{10}lg^{2}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{2}{10}lg^{3}(x)} - \frac{6lg(lg(x))}{x^{3}ln^{3}{10}lg^{4}(x)} + \frac{11}{x^{3}ln^{4}{10}lg^{4}(x)} + \frac{9}{x^{3}ln^{3}{10}lg^{3}(x)} + \frac{2}{x^{3}ln^{2}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-2*-3lg(lg(x))}{x^{4}ln{10}lg^{2}(x)} - \frac{2*-0lg(lg(x))}{x^{3}ln^{2}{10}lg^{2}(x)} - \frac{2}{x^{3}ln{10}ln{10}(lg(x))ln{10}(x)lg^{2}(x)} - \frac{2lg(lg(x))*-2}{x^{3}ln{10}lg^{3}(x)ln{10}(x)} - \frac{6*-3lg(lg(x))}{x^{4}ln^{2}{10}lg^{3}(x)} - \frac{6*-2*0lg(lg(x))}{x^{3}ln^{3}{10}lg^{3}(x)} - \frac{6}{x^{3}ln^{2}{10}ln{10}(lg(x))ln{10}(x)lg^{3}(x)} - \frac{6lg(lg(x))*-3}{x^{3}ln^{2}{10}lg^{4}(x)ln{10}(x)} - \frac{6*-3lg(lg(x))}{x^{4}ln^{3}{10}lg^{4}(x)} - \frac{6*-3*0lg(lg(x))}{x^{3}ln^{4}{10}lg^{4}(x)} - \frac{6}{x^{3}ln^{3}{10}ln{10}(lg(x))ln{10}(x)lg^{4}(x)} - \frac{6lg(lg(x))*-4}{x^{3}ln^{3}{10}lg^{5}(x)ln{10}(x)} + \frac{11*-3}{x^{4}ln^{4}{10}lg^{4}(x)} + \frac{11*-4*0}{x^{3}ln^{5}{10}lg^{4}(x)} + \frac{11*-4}{x^{3}ln^{4}{10}lg^{5}(x)ln{10}(x)} + \frac{9*-3}{x^{4}ln^{3}{10}lg^{3}(x)} + \frac{9*-3*0}{x^{3}ln^{4}{10}lg^{3}(x)} + \frac{9*-3}{x^{3}ln^{3}{10}lg^{4}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{2}{10}lg^{2}(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2*-2}{x^{3}ln^{2}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{6lg(lg(x))}{x^{4}ln{10}lg^{2}(x)} + \frac{22lg(lg(x))}{x^{4}ln^{2}{10}lg^{3}(x)} + \frac{36lg(lg(x))}{x^{4}ln^{3}{10}lg^{4}(x)} + \frac{24lg(lg(x))}{x^{4}ln^{4}{10}lg^{5}(x)} - \frac{33}{x^{4}ln^{3}{10}lg^{3}(x)} - \frac{50}{x^{4}ln^{5}{10}lg^{5}(x)} - \frac{66}{x^{4}ln^{4}{10}lg^{4}(x)} - \frac{6}{x^{4}ln^{2}{10}lg^{2}(x)}\\ \end{split}\end{equation} \]
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