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。
\[ \begin{equation}\begin{split}【1/1】求函数lg(lg(lg(lg(lg(x))))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg(lg(lg(lg(x)))))\right)}{dx}\\=&\frac{1}{ln{10}(lg(lg(lg(lg(x)))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)}\\=&\frac{1}{xln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))}\right)}{dx}\\=&\frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{-5*0}{xln^{6}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{-1}{xln^{5}{10}lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{-1}{xln^{5}{10}lg(lg(lg(lg(x))))lg^{2}(lg(x))ln{10}(lg(x))ln{10}(x)lg(x)lg(lg(lg(x)))} + \frac{-1}{xln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg^{2}(x)ln{10}(x)lg(lg(lg(x)))} + \frac{-1}{xln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)}\\=&\frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{1}{x^{2}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{1}{x^{2}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{1}{x^{2}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))}\right)}{dx}\\=&\frac{--2}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} - \frac{-5*0}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{5}{10}lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg(lg(x))lg(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg^{2}(lg(x))ln{10}(lg(x))ln{10}(x)lg(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg^{2}(x)ln{10}(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} - \frac{-2}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{-9*0}{x^{2}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{9}{10}lg^{3}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg^{2}(x)lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{3}(x)ln{10}(x)lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{3}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} - \frac{-2}{x^{3}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{-7*0}{x^{2}ln^{8}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{-2}{x^{2}ln^{7}{10}lg^{3}(x)ln{10}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{7}{10}lg^{2}(x)lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{-2}{x^{2}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} - \frac{-2}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{-6*0}{x^{2}ln^{7}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{6}{10}lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{-2}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg^{3}(x)ln{10}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg^{2}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(x)))} - \frac{-1}{x^{2}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} - \frac{-2}{x^{3}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{-8*0}{x^{2}ln^{9}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{8}{10}lg^{3}(x)ln{10}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{8}{10}lg^{2}(x)lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{-1}{x^{2}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(lg(x)))} - \frac{-2}{x^{2}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{3}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)}\\=&\frac{2}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3}{x^{3}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2}{x^{3}ln^{11}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{12}{10}lg^{3}(x)lg^{3}(lg(x))lg^{2}(lg(lg(lg(x))))lg^{3}(lg(lg(x)))} + \frac{3}{x^{3}ln^{8}{10}lg^{3}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{1}{x^{3}ln^{11}{10}lg^{3}(lg(x))lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{9}{10}lg(lg(lg(lg(x))))lg^{3}(x)lg^{3}(lg(x))lg(lg(lg(x)))} + \frac{1}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg(x))lg^{2}(lg(lg(x)))lg(lg(lg(lg(x))))} + \frac{1}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{3}(x)lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{7}{10}lg(lg(lg(lg(x))))lg^{3}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{9}{10}lg^{3}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{1}{x^{3}ln^{12}{10}lg^{3}(x)lg^{3}(lg(x))lg^{3}(lg(lg(x)))lg^{2}(lg(lg(lg(x))))} + \frac{2}{x^{3}ln^{11}{10}lg^{3}(x)lg(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(lg(lg(x)))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3}{x^{3}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2}{x^{3}ln^{11}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{12}{10}lg^{3}(x)lg^{3}(lg(x))lg^{2}(lg(lg(lg(x))))lg^{3}(lg(lg(x)))} + \frac{3}{x^{3}ln^{8}{10}lg^{3}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{1}{x^{3}ln^{11}{10}lg^{3}(lg(x))lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{9}{10}lg(lg(lg(lg(x))))lg^{3}(x)lg^{3}(lg(x))lg(lg(lg(x)))} + \frac{1}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg(x))lg^{2}(lg(lg(x)))lg(lg(lg(lg(x))))} + \frac{1}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{3}(x)lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{7}{10}lg(lg(lg(lg(x))))lg^{3}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3}{x^{3}ln^{9}{10}lg^{3}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{2}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{1}{x^{3}ln^{12}{10}lg^{3}(x)lg^{3}(lg(x))lg^{3}(lg(lg(x)))lg^{2}(lg(lg(lg(x))))} + \frac{2}{x^{3}ln^{11}{10}lg^{3}(x)lg(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(lg(lg(x)))}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{2*-5*0}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{2*-1}{x^{3}ln^{5}{10}lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg(lg(x))lg(x)lg(lg(lg(x)))} + \frac{2*-1}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg^{2}(lg(x))ln{10}(lg(x))ln{10}(x)lg(x)lg(lg(lg(x)))} + \frac{2*-1}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg^{2}(x)ln{10}(x)lg(lg(lg(x)))} + \frac{2*-1}{x^{3}ln^{5}{10}lg(lg(lg(lg(x))))lg(lg(x))lg(x)lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{3*-3}{x^{4}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3*-9*0}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{9}{10}lg^{3}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(x))lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg^{2}(x)lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{3}(x)ln{10}(x)lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{9}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(x)lg^{3}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{3*-3}{x^{4}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3*-7*0}{x^{3}ln^{8}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{7}{10}lg^{3}(x)ln{10}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{7}{10}lg^{2}(x)lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(x))lg(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{7}{10}lg^{2}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{3*-3}{x^{4}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3*-6*0}{x^{3}ln^{7}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{6}{10}lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{3}(x)ln{10}(x)lg(lg(x))lg(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg^{2}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{6}{10}lg(lg(lg(lg(x))))lg^{2}(x)lg(lg(x))lg^{2}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{3*-3}{x^{4}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{3*-8*0}{x^{3}ln^{9}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{8}{10}lg^{3}(x)ln{10}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{8}{10}lg^{2}(x)lg^{3}(lg(x))ln{10}(lg(x))ln{10}(x)lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} + \frac{3*-1}{x^{3}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg^{2}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(lg(x)))} + \frac{3*-2}{x^{3}ln^{8}{10}lg^{2}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{3}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{2*-3}{x^{4}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2*-13*0}{x^{3}ln^{14}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{13}{10}lg^{4}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{3}(lg(x))lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{4}(lg(x))ln{10}(lg(x))ln{10}(x)lg^{3}(x)lg^{3}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{4}(x)ln{10}(x)lg^{3}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{13}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(x)lg^{4}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{2*-3}{x^{4}ln^{11}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-11*0}{x^{3}ln^{12}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{11}{10}lg^{4}(x)ln{10}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-2}{x^{3}ln^{11}{10}lg^{3}(x)lg^{3}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{3}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{11}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{4}(lg(x))ln{10}(lg(x))ln{10}(x)lg^{2}(lg(lg(x)))} + \frac{2*-2}{x^{3}ln^{11}{10}lg^{3}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(lg(lg(x)))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)} + \frac{2*-3}{x^{4}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-10*0}{x^{3}ln^{11}{10}lg^{2}(lg(lg(lg(x))))lg^{3}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-2}{x^{3}ln^{10}{10}lg^{3}(lg(lg(lg(x))))ln{10}(lg(lg(lg(x))))ln{10}(lg(lg(x)))ln{10}(lg(x))ln{10}(x)lg^{3}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + \frac{2*-3}{x^{3}ln^{10}{10}lg^{2}(lg(lg(lg(x))))lg^{4}(x)ln{10}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} + 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\frac{6}{x^{4}ln^{14}{10}lg^{3}(lg(lg(lg(x))))lg^{4}(x)lg^{3}(lg(x))lg^{3}(lg(lg(x)))} - \frac{6}{x^{4}ln^{16}{10}lg^{4}(x)lg^{4}(lg(x))lg^{3}(lg(lg(lg(x))))lg^{4}(lg(lg(x)))} - \frac{12}{x^{4}ln^{12}{10}lg^{4}(x)lg^{2}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{2}(lg(lg(x)))} - \frac{4}{x^{4}ln^{15}{10}lg^{4}(lg(x))lg^{4}(x)lg^{3}(lg(lg(lg(x))))lg^{3}(lg(lg(x)))} - \frac{6}{x^{4}ln^{13}{10}lg^{2}(lg(lg(lg(x))))lg^{4}(x)lg^{4}(lg(x))lg^{2}(lg(lg(x)))} - \frac{9}{x^{4}ln^{14}{10}lg^{4}(x)lg^{4}(lg(x))lg^{3}(lg(lg(x)))lg^{2}(lg(lg(lg(x))))} - \frac{6}{x^{4}ln^{14}{10}lg^{3}(lg(lg(lg(x))))lg^{3}(lg(x))lg^{4}(x)lg^{3}(lg(lg(x)))} - \frac{9}{x^{4}ln^{11}{10}lg^{2}(lg(lg(lg(x))))lg^{4}(x)lg^{2}(lg(x))lg^{2}(lg(lg(x)))} - \frac{12}{x^{4}ln^{13}{10}lg^{4}(x)lg^{3}(lg(x))lg^{2}(lg(lg(lg(x))))lg^{3}(lg(lg(x)))} - \frac{6}{x^{4}ln^{14}{10}lg^{4}(x)lg^{4}(lg(x))lg^{2}(lg(lg(lg(x))))lg^{3}(lg(lg(x)))} - \frac{4}{x^{4}ln^{16}{10}lg^{4}(x)lg^{4}(lg(x))lg^{4}(lg(lg(x)))lg^{3}(lg(lg(lg(x))))} - \frac{6}{x^{4}ln^{15}{10}lg^{4}(x)lg^{2}(lg(lg(lg(x))))lg^{4}(lg(x))lg^{4}(lg(lg(x)))} - \frac{11}{x^{4}ln^{9}{10}lg^{4}(x)lg(lg(lg(lg(x))))lg^{2}(lg(x))lg(lg(lg(x)))} - \frac{6}{x^{4}ln^{12}{10}lg^{3}(lg(x))lg^{4}(x)lg^{2}(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{12}{x^{4}ln^{10}{10}lg(lg(lg(lg(x))))lg^{4}(x)lg^{3}(lg(x))lg(lg(lg(x)))} - \frac{6}{x^{4}ln^{11}{10}lg^{4}(x)lg^{3}(lg(x))lg^{2}(lg(lg(x)))lg(lg(lg(lg(x))))} - \frac{3}{x^{4}ln^{13}{10}lg^{4}(x)lg^{4}(lg(x))lg^{2}(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{2}{x^{4}ln^{15}{10}lg^{4}(x)lg^{4}(lg(x))lg^{3}(lg(lg(x)))lg^{3}(lg(lg(lg(x))))} - \frac{3}{x^{4}ln^{14}{10}lg^{4}(x)lg^{2}(lg(lg(lg(x))))lg^{4}(lg(x))lg^{3}(lg(lg(x)))} - \frac{2}{x^{4}ln^{13}{10}lg^{2}(lg(lg(lg(x))))lg^{4}(lg(x))lg^{4}(x)lg^{2}(lg(lg(x)))} - \frac{6}{x^{4}ln^{11}{10}lg^{4}(x)lg(lg(lg(lg(x))))lg^{4}(lg(x))lg(lg(lg(x)))} - \frac{8}{x^{4}ln^{12}{10}lg^{4}(x)lg^{4}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{3}{x^{4}ln^{12}{10}lg^{4}(x)lg^{4}(lg(x))lg^{2}(lg(lg(x)))lg(lg(lg(lg(x))))} - \frac{2}{x^{4}ln^{13}{10}lg^{4}(lg(x))lg^{3}(lg(lg(x)))lg^{4}(x)lg(lg(lg(lg(x))))} - \frac{2}{x^{4}ln^{11}{10}lg^{2}(lg(lg(lg(x))))lg^{2}(lg(x))lg^{4}(x)lg^{2}(lg(lg(x)))} - \frac{6}{x^{4}ln^{8}{10}lg(lg(lg(lg(x))))lg^{4}(x)lg(lg(x))lg(lg(lg(x)))} - \frac{11}{x^{4}ln^{10}{10}lg^{4}(x)lg^{2}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{12}{x^{4}ln^{11}{10}lg^{4}(x)lg^{3}(lg(x))lg(lg(lg(lg(x))))lg^{2}(lg(lg(x)))} - \frac{6}{x^{4}ln^{13}{10}lg^{4}(x)lg^{3}(lg(x))lg^{3}(lg(lg(x)))lg^{2}(lg(lg(lg(x))))} - \frac{12}{x^{4}ln^{12}{10}lg^{4}(x)lg(lg(lg(lg(x))))lg^{3}(lg(x))lg^{3}(lg(lg(x)))} - \frac{4}{x^{4}ln^{13}{10}lg^{4}(x)lg(lg(lg(lg(x))))lg^{4}(lg(x))lg^{3}(lg(lg(x)))} - \frac{3}{x^{4}ln^{15}{10}lg^{4}(lg(x))lg^{4}(lg(lg(x)))lg^{4}(x)lg^{2}(lg(lg(lg(x))))} - \frac{2}{x^{4}ln^{16}{10}lg^{4}(x)lg^{3}(lg(lg(lg(x))))lg^{4}(lg(x))lg^{4}(lg(lg(x)))} - \frac{2}{x^{4}ln^{15}{10}lg^{4}(lg(x))lg^{4}(x)lg^{2}(lg(lg(lg(x))))lg^{4}(lg(lg(x)))} - \frac{6}{x^{4}ln^{13}{10}lg(lg(lg(lg(x))))lg^{4}(x)lg^{4}(lg(x))lg^{3}(lg(lg(x)))} - \frac{6}{x^{4}ln^{14}{10}lg^{4}(x)lg^{4}(lg(x))lg^{4}(lg(lg(x)))lg(lg(lg(lg(x))))}\\ \end{split}\end{equation} \]

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