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 2 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数log_{2}^{log_{2}^{x}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{2}^{log_{2}^{x}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))}{(log_{2}^{x})} - \frac{(0)log_{2}^{log_{2}^{x}}}{(2)})}{(ln(2))})\\=&\frac{1}{xlog(2, x)ln^{2}(2)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xlog(2, x)ln^{2}(2)}\right)}{dx}\\=&\frac{-1}{x^{2}log(2, x)ln^{2}(2)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{xln^{2}(2)} + \frac{-2*0}{xlog(2, x)ln^{3}(2)(2)}\\=&\frac{-1}{x^{2}log(2, x)ln^{2}(2)} - \frac{1}{x^{2}{\left(log(2, x)^{2}ln^{3}(2)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}log(2, x)ln^{2}(2)} - \frac{1}{x^{2}{\left(log(2, x)^{2}ln^{3}(2)}\right)}{dx}\\=&\frac{--2}{x^{3}log(2, x)ln^{2}(2)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{x^{2}ln^{2}(2)} - \frac{-2*0}{x^{2}log(2, x)ln^{3}(2)(2)} - \frac{-2}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} - \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}ln^{3}(2)} - \frac{-3*0}{x^{2}{\left(log(2, x)^{2}ln^{4}(2)(2)}\\=&\frac{2}{x^{3}log(2, x)ln^{2}(2)} + \frac{3}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{2}{x^{3}{\left(log(2, x)^{3}ln^{4}(2)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}log(2, x)ln^{2}(2)} + \frac{3}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{2}{x^{3}{\left(log(2, x)^{3}ln^{4}(2)}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(2, x)ln^{2}(2)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{x^{3}ln^{2}(2)} + \frac{2*-2*0}{x^{3}log(2, x)ln^{3}(2)(2)} + \frac{3*-3}{x^{4}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}ln^{3}(2)} + \frac{3*-3*0}{x^{3}{\left(log(2, x)^{2}ln^{4}(2)(2)} + \frac{2*-3}{x^{4}{\left(log(2, x)^{3}ln^{4}(2)} + \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln^{4}(2)} + \frac{2*-4*0}{x^{3}{\left(log(2, x)^{3}ln^{5}(2)(2)}\\=&\frac{-6}{x^{4}log(2, x)ln^{2}(2)} - \frac{11}{x^{4}{\left(log(2, x)^{2}ln^{3}(2)} - \frac{12}{x^{4}{\left(log(2, x)^{3}ln^{4}(2)} - \frac{6}{x^{4}{\left(log(2, x)^{4}ln^{5}(2)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数lg(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg(x))\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)}\\=&\frac{1}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} + \frac{-2*0}{xln^{3}{10}lg(x)} + \frac{-1}{xln^{2}{10}lg^{2}(x)ln{10}(x)}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln^{2}{10}lg(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg(x)} - \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln^{2}{10}lg(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg(x)} + \frac{2*-1}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-6}{x^{4}ln^{2}{10}lg(x)} - \frac{11}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}ln^{5}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数log_{2}^{log_{2}^{x}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{2}^{log_{2}^{x}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))}))}{(log_{2}^{x})} - \frac{(0)log_{2}^{log_{2}^{x}}}{(2)})}{(ln(2))})\\=&\frac{1}{xlog(2, x)ln^{2}(2)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xlog(2, x)ln^{2}(2)}\right)}{dx}\\=&\frac{-1}{x^{2}log(2, x)ln^{2}(2)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{xln^{2}(2)} + \frac{-2*0}{xlog(2, x)ln^{3}(2)(2)}\\=&\frac{-1}{x^{2}log(2, x)ln^{2}(2)} - \frac{1}{x^{2}{\left(log(2, x)^{2}ln^{3}(2)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}log(2, x)ln^{2}(2)} - \frac{1}{x^{2}{\left(log(2, x)^{2}ln^{3}(2)}\right)}{dx}\\=&\frac{--2}{x^{3}log(2, x)ln^{2}(2)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{x^{2}ln^{2}(2)} - \frac{-2*0}{x^{2}log(2, x)ln^{3}(2)(2)} - \frac{-2}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} - \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}ln^{3}(2)} - \frac{-3*0}{x^{2}{\left(log(2, x)^{2}ln^{4}(2)(2)}\\=&\frac{2}{x^{3}log(2, x)ln^{2}(2)} + \frac{3}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{2}{x^{3}{\left(log(2, x)^{3}ln^{4}(2)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}log(2, x)ln^{2}(2)} + \frac{3}{x^{3}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{2}{x^{3}{\left(log(2, x)^{3}ln^{4}(2)}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(2, x)ln^{2}(2)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{2}(ln(2))})}{x^{3}ln^{2}(2)} + \frac{2*-2*0}{x^{3}log(2, x)ln^{3}(2)(2)} + \frac{3*-3}{x^{4}{\left(log(2, x)^{2}ln^{3}(2)} + \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}ln^{3}(2)} + \frac{3*-3*0}{x^{3}{\left(log(2, x)^{2}ln^{4}(2)(2)} + \frac{2*-3}{x^{4}{\left(log(2, x)^{3}ln^{4}(2)} + \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln^{4}(2)} + \frac{2*-4*0}{x^{3}{\left(log(2, x)^{3}ln^{5}(2)(2)}\\=&\frac{-6}{x^{4}log(2, x)ln^{2}(2)} - \frac{11}{x^{4}{\left(log(2, x)^{2}ln^{3}(2)} - \frac{12}{x^{4}{\left(log(2, x)^{3}ln^{4}(2)} - \frac{6}{x^{4}{\left(log(2, x)^{4}ln^{5}(2)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数lg(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg(x))\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)}\\=&\frac{1}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} + \frac{-2*0}{xln^{3}{10}lg(x)} + \frac{-1}{xln^{2}{10}lg^{2}(x)ln{10}(x)}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln^{2}{10}lg(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg(x)} - \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln^{2}{10}lg(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg(x)} + \frac{2*-1}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-6}{x^{4}ln^{2}{10}lg(x)} - \frac{11}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}ln^{5}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
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