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。
\[ \begin{equation}\begin{split}【1/1】求函数ln(ln(ln(ln(ln(x))))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(ln(ln(ln(ln(x)))))\right)}{dx}\\=&\frac{1}{(ln(ln(ln(ln(x)))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)}\\=&\frac{1}{xln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{-1}{xln^{2}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{-1}{xln(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(x)} + \frac{-1}{xln(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(x)} + \frac{-1}{xln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(x)(x)}\\=&\frac{-1}{x^{2}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} - \frac{1}{x^{2}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} - \frac{1}{x^{2}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{1}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))}\right)}{dx}\\=&\frac{--2}{x^{3}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} - \frac{-1}{x^{2}ln^{2}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} - \frac{-1}{x^{2}ln(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(x)} - \frac{-1}{x^{2}ln(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(x)} - \frac{-1}{x^{2}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(x)(x)} - \frac{-2}{x^{3}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{-2}{x^{2}ln^{3}(ln(x))(ln(x))(x)ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{-2}{x^{2}ln^{2}(ln(x))ln^{3}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{-1}{x^{2}ln^{2}(ln(x))ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))} - \frac{-1}{x^{2}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} - \frac{-2}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{-2}{x^{2}ln^{3}(x)(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{-2}{x^{2}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{-2}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} - \frac{-2}{x^{2}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} - \frac{-2}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{-2}{x^{2}ln^{3}(x)(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{-1}{x^{2}ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{-2}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))} - \frac{-2}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} - \frac{-2}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} - \frac{-2}{x^{2}ln^{3}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} - \frac{-1}{x^{2}ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(ln(x))} - \frac{-1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(ln(x))} - \frac{-1}{x^{2}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(ln(x))(ln(x))(x)}\\=&\frac{2}{x^{3}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{3}{x^{3}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{2}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{1}{x^{3}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} + \frac{1}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2}{x^{3}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))} + \frac{3}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} + \frac{2}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{1}{x^{3}ln^{3}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{3}{x^{3}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{3}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{2}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{1}{x^{3}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} + \frac{1}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2}{x^{3}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))} + \frac{3}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} + \frac{2}{x^{3}ln^{3}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} + \frac{2}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{1}{x^{3}ln^{3}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{2*-1}{x^{3}ln^{2}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} + \frac{2*-1}{x^{3}ln(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(x)} + \frac{2*-1}{x^{3}ln(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(x)} + \frac{2*-1}{x^{3}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(x)(x)} + \frac{3*-3}{x^{4}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{3}(ln(x))(ln(x))(x)ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{2}(ln(x))ln^{3}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{3*-1}{x^{3}ln^{2}(ln(x))ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))} + \frac{3*-1}{x^{3}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{3}(x)(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{2}(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{3}(x)(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-1}{x^{3}ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{3*-2}{x^{3}ln^{3}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(ln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(ln(x))} + \frac{3*-1}{x^{3}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(ln(x))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(ln(x))ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{4}(ln(x))(ln(x))(x)ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{3}(ln(x))ln^{4}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-1}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))} + \frac{2*-1}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{-3}{x^{4}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} + \frac{-2}{x^{3}ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} + \frac{-3}{x^{3}ln^{2}(ln(ln(x)))ln^{4}(x)(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} + \frac{-3}{x^{3}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} + \frac{-2}{x^{3}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{-3}{x^{4}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} + \frac{-3}{x^{3}ln^{4}(ln(x))(ln(x))(x)ln^{3}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} + \frac{-3}{x^{3}ln^{3}(ln(x))ln^{4}(x)(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} + \frac{-2}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(ln(ln(ln(x))))} + \frac{-1}{x^{3}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2*-3}{x^{3}ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{2*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} + \frac{2*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-3}{x^{3}ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} + \frac{3*-3}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{4}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(ln(x))))} + \frac{3*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{3}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{4}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{3}(ln(ln(ln(x))))ln^{4}(ln(x))(ln(x))(x)ln^{3}(x)ln^{3}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{4}(x)(x)ln^{3}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{3}(x)ln^{4}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{3*-3}{x^{4}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-3}{x^{3}ln^{4}(x)(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-1}{x^{3}ln^{3}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln^{3}(ln(x))(ln(x))(x)ln^{2}(ln(ln(x)))} + \frac{3*-2}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} + \frac{2*-3}{x^{3}ln^{3}(x)ln^{4}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(ln(x)))} + \frac{2*-2}{x^{3}ln^{3}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{3}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} + \frac{2*-3}{x^{3}ln^{3}(x)ln^{4}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(ln(ln(ln(x))))ln^{3}(ln(x))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln^{3}(ln(x))} + \frac{2*-3}{x^{3}ln^{3}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{4}(ln(x))(ln(x))(x)} + \frac{2*-3}{x^{4}ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{2*-3}{x^{3}ln^{4}(x)(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} + \frac{2*-1}{x^{3}ln^{3}(x)ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)ln(ln(ln(x)))ln(ln(x))} + \frac{2*-1}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln(ln(x))} + \frac{2*-1}{x^{3}ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln^{2}(ln(x))(ln(x))(x)} + \frac{-3}{x^{4}ln^{3}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))} + \frac{-3}{x^{3}ln^{4}(x)(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))} + \frac{-1}{x^{3}ln^{3}(x)ln^{2}(ln(ln(x)))(ln(ln(x)))(ln(x))(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))} + \frac{-2}{x^{3}ln^{3}(x)ln(ln(ln(x)))ln^{3}(ln(x))(ln(x))(x)ln(ln(ln(ln(x))))} + \frac{-1}{x^{3}ln^{3}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln^{2}(ln(ln(ln(x))))(ln(ln(ln(x))))(ln(ln(x)))(ln(x))(x)}\\=&\frac{-6}{x^{4}ln(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(x)} - \frac{11}{x^{4}ln^{2}(ln(x))ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{11}{x^{4}ln^{2}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{11}{x^{4}ln^{2}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{11}{x^{4}ln^{2}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} - \frac{12}{x^{4}ln^{3}(ln(x))ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{12}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{6}{x^{4}ln^{2}(ln(ln(x)))ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{3}(ln(x))ln^{3}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} - \frac{18}{x^{4}ln^{3}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{12}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{18}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{12}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{3}(x)ln^{3}(ln(ln(x)))} - \frac{18}{x^{4}ln^{3}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{12}{x^{4}ln^{3}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} - \frac{12}{x^{4}ln^{3}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} - \frac{12}{x^{4}ln^{3}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} - \frac{6}{x^{4}ln^{3}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{4}(ln(x))ln^{4}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{10}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{2}{x^{4}ln^{2}(ln(ln(x)))ln^{4}(x)ln^{4}(ln(x))ln^{2}(ln(ln(ln(x))))} - \frac{5}{x^{4}ln^{4}(ln(x))ln^{4}(x)ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{4}(x)ln^{2}(ln(x))ln(ln(ln(ln(x))))ln(ln(ln(x)))} - \frac{2}{x^{4}ln^{2}(ln(ln(x)))ln^{4}(x)ln^{2}(ln(ln(ln(x))))ln^{3}(ln(x))} - \frac{2}{x^{4}ln^{4}(x)ln^{2}(ln(ln(x)))ln^{3}(ln(x))ln(ln(ln(ln(x))))} - \frac{2}{x^{4}ln^{4}(ln(x))ln^{4}(x)ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{3}{x^{4}ln^{4}(x)ln^{2}(ln(ln(x)))ln^{3}(ln(x))ln^{2}(ln(ln(ln(x))))} - \frac{3}{x^{4}ln^{2}(ln(ln(x)))ln^{4}(ln(x))ln^{4}(x)ln^{2}(ln(ln(ln(x))))} - \frac{2}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{4}(x)ln^{3}(ln(ln(x)))ln^{4}(ln(x))} - \frac{3}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln(ln(ln(ln(x))))} - \frac{2}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))} - \frac{1}{x^{4}ln^{2}(ln(ln(ln(x))))ln^{4}(x)ln^{3}(ln(ln(x)))ln^{4}(ln(x))} - \frac{11}{x^{4}ln^{4}(x)ln^{2}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{18}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{3}(ln(x))ln^{4}(x)ln^{3}(ln(ln(x)))} - \frac{6}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln^{2}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{13}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln^{3}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{4}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{4}(ln(x))ln^{4}(x)ln^{3}(ln(ln(x)))} - \frac{9}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln^{4}(ln(ln(x)))ln^{2}(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{4}(ln(x))ln^{4}(x)ln^{4}(ln(ln(x)))} - \frac{6}{x^{4}ln^{4}(ln(x))ln^{4}(ln(ln(ln(x))))ln^{4}(ln(ln(x)))ln^{4}(x)} - \frac{6}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{4}(x)ln^{4}(ln(x))ln^{3}(ln(ln(x)))} - \frac{6}{x^{4}ln^{3}(ln(x))ln^{3}(ln(ln(ln(x))))ln^{4}(x)ln^{3}(ln(ln(x)))} - \frac{6}{x^{4}ln^{3}(ln(ln(ln(x))))ln^{4}(x)ln^{4}(ln(ln(x)))ln^{4}(ln(x))} - \frac{11}{x^{4}ln^{4}(x)ln(ln(ln(ln(x))))ln^{2}(ln(x))ln^{2}(ln(ln(x)))} - \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} - \frac{12}{x^{4}ln^{4}(x)ln^{3}(ln(ln(x)))ln(ln(ln(ln(x))))ln^{3}(ln(x))} - \frac{6}{x^{4}ln^{4}(x)ln^{4}(ln(x))ln(ln(ln(ln(x))))ln^{2}(ln(ln(x)))} - \frac{2}{x^{4}ln^{3}(ln(ln(x)))ln^{4}(x)ln^{2}(ln(ln(ln(x))))ln^{4}(ln(x))} - \frac{4}{x^{4}ln^{4}(x)ln^{3}(ln(ln(x)))ln^{4}(ln(x))ln(ln(ln(ln(x))))} - \frac{6}{x^{4}ln^{4}(ln(x))ln^{4}(ln(ln(x)))ln^{4}(x)ln(ln(ln(ln(x))))} - \frac{2}{x^{4}ln^{4}(ln(ln(x)))ln^{4}(x)ln^{2}(ln(ln(ln(x))))ln^{4}(ln(x))} - \frac{6}{x^{4}ln^{4}(x)ln(ln(ln(ln(x))))ln^{4}(ln(x))ln^{3}(ln(ln(x)))} - \frac{6}{x^{4}ln^{4}(x)ln(ln(ln(ln(x))))ln(ln(ln(x)))ln(ln(x))} - \frac{5}{x^{4}ln^{4}(x)ln(ln(ln(x)))ln^{2}(ln(x))ln(ln(ln(ln(x))))} - \frac{1}{x^{4}ln^{3}(ln(x))ln^{2}(ln(ln(x)))ln^{4}(x)ln(ln(ln(ln(x))))} - \frac{2}{x^{4}ln^{4}(x)ln^{3}(ln(x))ln(ln(ln(x)))ln(ln(ln(ln(x))))} - \frac{1}{x^{4}ln^{2}(ln(ln(ln(x))))ln^{2}(ln(ln(x)))ln^{4}(x)ln^{3}(ln(x))}\\ \end{split}\end{equation} \]
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