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。
\[ \begin{equation}\begin{split}【1/1】求函数{lg({lg(x)}^{2})}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg^{2}(lg^{2}(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg^{2}(lg^{2}(x))\right)}{dx}\\=&\frac{2lg(lg^{2}(x))*2lg(x)}{ln{10}(lg^{2}(x))ln{10}(x)}\\=&\frac{4lg(lg^{2}(x))}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{4lg(lg^{2}(x))}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{4*-lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} + \frac{4*-2*0lg(lg^{2}(x))}{xln^{3}{10}lg(x)} + \frac{4*-lg(lg^{2}(x))}{xln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{4*2lg(x)}{xln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)}\\=&\frac{-4lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} - \frac{4lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{8}{x^{2}ln^{4}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} - \frac{4lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{8}{x^{2}ln^{4}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-4*-2lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} - \frac{4*-2*0lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg(x)} - \frac{4*-lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{4*2lg(x)}{x^{2}ln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)} - \frac{4*-2lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{4*-3*0lg(lg^{2}(x))}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{4*-2lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)} - \frac{4*2lg(x)}{x^{2}ln^{3}{10}lg^{2}(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{8*-2}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{8*-4*0}{x^{2}ln^{5}{10}lg^{2}(x)} + \frac{8*-2}{x^{2}ln^{4}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{8lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} + \frac{12lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{8lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{3}(x)} - \frac{24}{x^{3}ln^{4}{10}lg^{2}(x)} - \frac{24}{x^{3}ln^{5}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{8lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} + \frac{12lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{8lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{3}(x)} - \frac{24}{x^{3}ln^{4}{10}lg^{2}(x)} - \frac{24}{x^{3}ln^{5}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{8*-3lg(lg^{2}(x))}{x^{4}ln^{2}{10}lg(x)} + \frac{8*-2*0lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg(x)} + \frac{8*-lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{8*2lg(x)}{x^{3}ln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{12*-3lg(lg^{2}(x))}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{12*-3*0lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{12*-2lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{12*2lg(x)}{x^{3}ln^{3}{10}lg^{2}(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{8*-3lg(lg^{2}(x))}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{8*-4*0lg(lg^{2}(x))}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{8*-3lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)} + \frac{8*2lg(x)}{x^{3}ln^{4}{10}lg^{3}(x)ln{10}(lg^{2}(x))ln{10}(x)} - \frac{24*-3}{x^{4}ln^{4}{10}lg^{2}(x)} - \frac{24*-4*0}{x^{3}ln^{5}{10}lg^{2}(x)} - \frac{24*-2}{x^{3}ln^{4}{10}lg^{3}(x)ln{10}(x)} - \frac{24*-3}{x^{4}ln^{5}{10}lg^{3}(x)} - \frac{24*-5*0}{x^{3}ln^{6}{10}lg^{3}(x)} - \frac{24*-3}{x^{3}ln^{5}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-24lg(lg^{2}(x))}{x^{4}ln^{2}{10}lg(x)} - \frac{44lg(lg^{2}(x))}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{48lg(lg^{2}(x))}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{24lg(lg^{2}(x))}{x^{4}ln^{5}{10}lg^{4}(x)} + \frac{144}{x^{4}ln^{5}{10}lg^{3}(x)} + \frac{88}{x^{4}ln^{4}{10}lg^{2}(x)} + \frac{88}{x^{4}ln^{6}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{lg({lg(x)}^{2})}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg^{2}(lg^{2}(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg^{2}(lg^{2}(x))\right)}{dx}\\=&\frac{2lg(lg^{2}(x))*2lg(x)}{ln{10}(lg^{2}(x))ln{10}(x)}\\=&\frac{4lg(lg^{2}(x))}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{4lg(lg^{2}(x))}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{4*-lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} + \frac{4*-2*0lg(lg^{2}(x))}{xln^{3}{10}lg(x)} + \frac{4*-lg(lg^{2}(x))}{xln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{4*2lg(x)}{xln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)}\\=&\frac{-4lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} - \frac{4lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{8}{x^{2}ln^{4}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg(x)} - \frac{4lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{2}(x)} + \frac{8}{x^{2}ln^{4}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{-4*-2lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} - \frac{4*-2*0lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg(x)} - \frac{4*-lg(lg^{2}(x))}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{4*2lg(x)}{x^{2}ln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)} - \frac{4*-2lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{4*-3*0lg(lg^{2}(x))}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{4*-2lg(lg^{2}(x))}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)} - \frac{4*2lg(x)}{x^{2}ln^{3}{10}lg^{2}(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{8*-2}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{8*-4*0}{x^{2}ln^{5}{10}lg^{2}(x)} + \frac{8*-2}{x^{2}ln^{4}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{8lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} + \frac{12lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{8lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{3}(x)} - \frac{24}{x^{3}ln^{4}{10}lg^{2}(x)} - \frac{24}{x^{3}ln^{5}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{8lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg(x)} + \frac{12lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{8lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{3}(x)} - \frac{24}{x^{3}ln^{4}{10}lg^{2}(x)} - \frac{24}{x^{3}ln^{5}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{8*-3lg(lg^{2}(x))}{x^{4}ln^{2}{10}lg(x)} + \frac{8*-2*0lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg(x)} + \frac{8*-lg(lg^{2}(x))}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{8*2lg(x)}{x^{3}ln^{2}{10}lg(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{12*-3lg(lg^{2}(x))}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{12*-3*0lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{12*-2lg(lg^{2}(x))}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{12*2lg(x)}{x^{3}ln^{3}{10}lg^{2}(x)ln{10}(lg^{2}(x))ln{10}(x)} + \frac{8*-3lg(lg^{2}(x))}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{8*-4*0lg(lg^{2}(x))}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{8*-3lg(lg^{2}(x))}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)} + \frac{8*2lg(x)}{x^{3}ln^{4}{10}lg^{3}(x)ln{10}(lg^{2}(x))ln{10}(x)} - \frac{24*-3}{x^{4}ln^{4}{10}lg^{2}(x)} - \frac{24*-4*0}{x^{3}ln^{5}{10}lg^{2}(x)} - \frac{24*-2}{x^{3}ln^{4}{10}lg^{3}(x)ln{10}(x)} - \frac{24*-3}{x^{4}ln^{5}{10}lg^{3}(x)} - \frac{24*-5*0}{x^{3}ln^{6}{10}lg^{3}(x)} - \frac{24*-3}{x^{3}ln^{5}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-24lg(lg^{2}(x))}{x^{4}ln^{2}{10}lg(x)} - \frac{44lg(lg^{2}(x))}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{48lg(lg^{2}(x))}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{24lg(lg^{2}(x))}{x^{4}ln^{5}{10}lg^{4}(x)} + \frac{144}{x^{4}ln^{5}{10}lg^{3}(x)} + \frac{88}{x^{4}ln^{4}{10}lg^{2}(x)} + \frac{88}{x^{4}ln^{6}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
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