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。
\[ \begin{equation}\begin{split}【1/1】求函数lg({(lg({(lg({(lg(x))}^{4}))}^{4}))}^{4}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg(lg^{4}(lg^{4}(lg^{4}(x))))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg^{4}(lg^{4}(lg^{4}(x))))\right)}{dx}\\=&\frac{4lg^{3}(lg^{4}(lg^{4}(x)))*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{ln{10}(lg^{4}(lg^{4}(lg^{4}(x))))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)}\\=&\frac{64}{xln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{64}{xln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))}\right)}{dx}\\=&\frac{64*-1}{x^{2}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{64*-4*0}{xln^{5}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{64*-4lg^{3}(x)}{xln^{4}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{64*-1}{xln^{4}{10}lg(lg^{4}(x))lg^{2}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{64*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{xln^{4}{10}lg(lg^{4}(x))lg(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)}\\=&\frac{-64}{x^{2}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{256}{x^{2}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{64}{x^{2}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{1024}{x^{2}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-64}{x^{2}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{256}{x^{2}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{64}{x^{2}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{1024}{x^{2}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))}\right)}{dx}\\=&\frac{-64*-2}{x^{3}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-4*0}{x^{2}ln^{5}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-4lg^{3}(x)}{x^{2}ln^{4}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-1}{x^{2}ln^{4}{10}lg(lg^{4}(x))lg^{2}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{2}ln^{4}{10}lg(lg^{4}(x))lg(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} - \frac{256*-2}{x^{3}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{256*-6*0}{x^{2}ln^{7}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{256*-2}{x^{2}ln^{6}{10}lg^{3}(x)ln{10}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{256*-2*4lg^{3}(x)}{x^{2}ln^{6}{10}lg^{2}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{256*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{2}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} - \frac{64*-2}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-5*0}{x^{2}ln^{6}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-4lg^{3}(x)}{x^{2}ln^{5}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-2}{x^{2}ln^{5}{10}lg(lg^{4}(x))lg^{3}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{64*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{2}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} - \frac{1024*-2}{x^{3}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} - \frac{1024*-7*0}{x^{2}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} - \frac{1024*-2*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{2}ln^{7}{10}lg^{3}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)lg^{2}(x)lg^{2}(lg^{4}(x))} - \frac{1024*-2}{x^{2}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)ln{10}(x)lg^{2}(lg^{4}(x))} - \frac{1024*-2*4lg^{3}(x)}{x^{2}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)}\\=&\frac{128}{x^{3}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{768}{x^{3}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{192}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{3072}{x^{3}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} + \frac{768}{x^{3}ln^{7}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{2048}{x^{3}ln^{8}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{4096}{x^{3}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{3}(x)} + \frac{128}{x^{3}ln^{6}{10}lg(lg^{4}(x))lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{3072}{x^{3}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{2}(lg^{4}(x))} + \frac{32768}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{8192}{x^{3}ln^{9}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{128}{x^{3}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{768}{x^{3}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{192}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{3072}{x^{3}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} + \frac{768}{x^{3}ln^{7}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{2048}{x^{3}ln^{8}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{4096}{x^{3}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{3}(x)} + \frac{128}{x^{3}ln^{6}{10}lg(lg^{4}(x))lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{3072}{x^{3}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{2}(lg^{4}(x))} + \frac{32768}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{8192}{x^{3}ln^{9}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))}\right)}{dx}\\=&\frac{128*-3}{x^{4}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-4*0}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-4lg^{3}(x)}{x^{3}ln^{4}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-1}{x^{3}ln^{4}{10}lg(lg^{4}(x))lg^{2}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{4}{10}lg(lg^{4}(x))lg(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{768*-3}{x^{4}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-6*0}{x^{3}ln^{7}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-2}{x^{3}ln^{6}{10}lg^{3}(x)ln{10}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-2*4lg^{3}(x)}{x^{3}ln^{6}{10}lg^{2}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{768*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{192*-3}{x^{4}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{192*-5*0}{x^{3}ln^{6}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{192*-4lg^{3}(x)}{x^{3}ln^{5}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{192*-2}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg^{3}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{192*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{3072*-3}{x^{4}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-7*0}{x^{3}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-2*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{7}{10}lg^{3}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)lg^{2}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-2}{x^{3}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)ln{10}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-2*4lg^{3}(x)}{x^{3}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{768*-3}{x^{4}ln^{7}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-7*0}{x^{3}ln^{8}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-3}{x^{3}ln^{7}{10}lg^{4}(x)ln{10}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{768*-2*4lg^{3}(x)}{x^{3}ln^{7}{10}lg^{3}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{768*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{7}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{2048*-3}{x^{4}ln^{8}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{2048*-8*0}{x^{3}ln^{9}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{2048*-3}{x^{3}ln^{8}{10}lg^{4}(x)ln{10}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} + \frac{2048*-3*4lg^{3}(x)}{x^{3}ln^{8}{10}lg^{3}(x)lg^{4}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{2048*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{8}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{4096*-3}{x^{4}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{3}(x)} + \frac{4096*-9*0}{x^{3}ln^{10}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{3}(x)} + \frac{4096*-2*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{9}{10}lg^{3}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(lg^{4}(x))lg^{3}(x)} + \frac{4096*-3*4lg^{3}(x)}{x^{3}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(x)} + \frac{4096*-3}{x^{3}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{4}(x)ln{10}(x)} + \frac{128*-3}{x^{4}ln^{6}{10}lg(lg^{4}(x))lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-6*0}{x^{3}ln^{7}{10}lg(lg^{4}(x))lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-4lg^{3}(x)}{x^{3}ln^{6}{10}lg^{2}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-3}{x^{3}ln^{6}{10}lg(lg^{4}(x))lg^{4}(x)ln{10}(x)lg(lg^{4}(lg^{4}(x)))} + \frac{128*-4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{6}{10}lg(lg^{4}(x))lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{3072*-3}{x^{4}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-8*0}{x^{3}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-2*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{8}{10}lg^{3}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-3}{x^{3}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(x)ln{10}(x)lg^{2}(lg^{4}(x))} + \frac{3072*-2*4lg^{3}(x)}{x^{3}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{3}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{32768*-3}{x^{4}ln^{10}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{32768*-10*0}{x^{3}ln^{11}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{32768*-3}{x^{3}ln^{10}{10}lg^{4}(x)ln{10}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{32768*-3*4lg^{3}(x)}{x^{3}ln^{10}{10}lg^{3}(x)lg^{4}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(lg^{4}(lg^{4}(x)))} + \frac{32768*-3*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{10}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{4}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)} + \frac{8192*-3}{x^{4}ln^{9}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))} + \frac{8192*-9*0}{x^{3}ln^{10}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))} + \frac{8192*-3}{x^{3}ln^{9}{10}lg^{4}(x)ln{10}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))} + \frac{8192*-2*4lg^{3}(lg^{4}(x))*4lg^{3}(x)}{x^{3}ln^{9}{10}lg^{3}(x)lg^{3}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(lg^{4}(x)))ln{10}(lg^{4}(x))ln{10}(x)lg^{3}(lg^{4}(x))} + \frac{8192*-3*4lg^{3}(x)}{x^{3}ln^{9}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(lg^{4}(x))ln{10}(lg^{4}(x))ln{10}(x)}\\=&\frac{-384}{x^{4}ln^{4}{10}lg(lg^{4}(x))lg(x)lg(lg^{4}(lg^{4}(x)))} - \frac{2816}{x^{4}ln^{6}{10}lg^{2}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{704}{x^{4}ln^{5}{10}lg(lg^{4}(x))lg^{2}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{11264}{x^{4}ln^{7}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(x)lg^{2}(lg^{4}(x))} - \frac{4608}{x^{4}ln^{7}{10}lg^{3}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{12288}{x^{4}ln^{8}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{24576}{x^{4}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{3}(x)} - \frac{768}{x^{4}ln^{6}{10}lg(lg^{4}(x))lg^{3}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{18432}{x^{4}ln^{8}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(x)lg^{2}(lg^{4}(x))} - \frac{196608}{x^{4}ln^{10}{10}lg^{3}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} - \frac{49152}{x^{4}ln^{9}{10}lg^{3}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))} - \frac{2816}{x^{4}ln^{8}{10}lg^{4}(x)lg^{2}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{12288}{x^{4}ln^{9}{10}lg^{4}(x)lg^{3}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{12288}{x^{4}ln^{10}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))lg^{4}(x)} - \frac{24576}{x^{4}ln^{10}{10}lg^{4}(x)lg^{4}(lg^{4}(x))lg(lg^{4}(lg^{4}(x)))} - \frac{32768}{x^{4}ln^{11}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(lg^{4}(x))lg^{4}(x)} - \frac{524288}{x^{4}ln^{12}{10}lg^{4}(x)lg^{4}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} - \frac{49152}{x^{4}ln^{11}{10}lg^{4}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(lg^{4}(x))} - \frac{12288}{x^{4}ln^{10}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(x)lg^{3}(lg^{4}(x))} - \frac{384}{x^{4}ln^{7}{10}lg(lg^{4}(x))lg^{4}(x)lg(lg^{4}(lg^{4}(x)))} - \frac{2048}{x^{4}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{2}(lg^{4}(x))lg^{4}(x)} - \frac{196608}{x^{4}ln^{11}{10}lg^{4}(x)lg^{3}(lg^{4}(x))lg^{3}(lg^{4}(lg^{4}(x)))} - \frac{9216}{x^{4}ln^{9}{10}lg^{2}(lg^{4}(lg^{4}(x)))lg^{4}(x)lg^{2}(lg^{4}(x))} - \frac{49152}{x^{4}ln^{10}{10}lg^{4}(x)lg^{2}(lg^{4}(lg^{4}(x)))lg^{3}(lg^{4}(x))} - \frac{1572864}{x^{4}ln^{13}{10}lg^{4}(lg^{4}(lg^{4}(x)))lg^{4}(lg^{4}(x))lg^{4}(x)} - \frac{262144}{x^{4}ln^{12}{10}lg^{4}(lg^{4}(x))lg^{4}(x)lg^{3}(lg^{4}(lg^{4}(x)))} - \frac{98304}{x^{4}ln^{11}{10}lg^{4}(x)lg^{4}(lg^{4}(x))lg^{2}(lg^{4}(lg^{4}(x)))}\\ \end{split}\end{equation} \]

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