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。
\[ \begin{equation}\begin{split}【1/1】求函数{lg(log_{1}^{x})}^{lg(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {lg(log_{1}^{x})}^{lg(x)}\right)}{dx}\\=&({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))\\=&\frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{xln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{xlog(1, x)ln(1)ln{10}lg(log_{1}^{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{xln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{xlog(1, x)ln(1)ln{10}lg(log_{1}^{x})}\right)}{dx}\\=&\frac{-{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{2}ln{10}} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{xln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0}{xln^{2}{10}} + \frac{-{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{xlog(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})lg(x)}{xln(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{xlog(1, x)ln^{2}(1)(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{xlog(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{xlog(1, x)ln(1)ln{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}}{xlog(1, x)ln(1)ln{10}lg(log_{1}^{x})ln{10}(x)}\\=&\frac{-{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{2}ln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{2}ln^{2}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}}{x^{2}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{2}ln{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{2}ln^{2}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}}{x^{2}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})}\right)}{dx}\\=&\frac{--2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}ln{10}} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{x^{2}ln{10}} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{2}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln{10}} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0}{x^{2}ln^{2}{10}} + \frac{-2{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{3}ln^{2}{10}} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln^{2}(lg(log_{1}^{x}))}{x^{2}ln^{2}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0ln^{2}(lg(log_{1}^{x}))}{x^{2}ln^{3}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}*2ln(lg(log_{1}^{x}))(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{2}ln^{2}{10}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})} + \frac{-2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{2}ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-0ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{2}log(1, x)ln^{2}{10}ln(1)ln{10}(x)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{2}log(1, x)ln^{2}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{-2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg(x)}{x^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{3}(1)(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})ln{10}(x)} - \frac{-2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{2}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})lg(x)}{x^{2}ln(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{x^{2}log(1, x)ln^{2}(1)(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{x^{2}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}log(1, x)ln(1)ln{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}}{x^{2}log(1, x)ln(1)ln{10}lg(log_{1}^{x})ln{10}(x)} + \frac{-2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{2}ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}log(1, x)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2*0lg(x)}{x^{2}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0lg(x)}{x^{2}log(1, x)ln^{2}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}log(1, x)ln^{2}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{2}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})ln{10}(x)} + \frac{-2{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg^{2}(x)}{x^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*2lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} - \frac{-2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg(x)}{x^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}}{x^{2}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{2*-2{lg(log_{1}^{x})}^{lg(x)}}{x^{3}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))}{x^{2}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})}{x^{2}ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-0}{x^{2}log(1, x)ln^{2}(1)(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-2*0}{x^{2}log(1, x)ln(1)ln^{3}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{2}log(1, x)ln(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})}\\=&\frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}ln{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{3}ln^{2}{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}{10}ln^{2}(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}}{x^{3}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}ln{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{3}ln^{2}{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}{10}ln^{2}(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}}{x^{3}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})}\right)}{dx}\\=&\frac{2*-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}ln{10}} + \frac{2({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{x^{3}ln{10}} + \frac{2{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln{10}} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0}{x^{3}ln^{2}{10}} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{4}ln^{2}{10}} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln^{2}(lg(log_{1}^{x}))}{x^{3}ln^{2}{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0ln^{2}(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*2ln(lg(log_{1}^{x}))(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}ln^{2}{10}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-0ln(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{2}{10}ln^{2}(1)(1)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}log(1, x)ln^{2}{10}ln(1)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{2}{10}ln(1)ln{10}(x)lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{2}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{4*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{4({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg(x)}{x^{3}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}*-3*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))}{x^{4}ln^{3}{10}} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln^{3}(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0ln^{3}(lg(log_{1}^{x}))}{x^{3}ln^{4}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}*3ln^{2}(lg(log_{1}^{x}))(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}ln^{3}{10}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-0ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*2ln(lg(log_{1}^{x}))(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)ln{10}(x)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}ln{10}(x)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - 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\frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}{\left(log(1, x)^{2}ln^{2}{10}ln^{2}(1)lg(log_{1}^{x})ln{10}(x)} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{4}(ln(1))})lg^{2}(x)}{x^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{4}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*2lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{4}(ln(1))})lg(x)}{x^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3*0lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{4}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{2*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{2({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})lg(x)}{x^{3}ln(1)ln{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{x^{3}log(1, x)ln^{2}(1)(1)ln{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-0lg(x)}{x^{3}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}log(1, x)ln(1)ln{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}}{x^{3}log(1, x)ln(1)ln{10}lg(log_{1}^{x})ln{10}(x)} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg^{2}(x)}{x^{3}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*2lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg(x)}{x^{3}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{2*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{2({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})lg(x)}{x^{3}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-3*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-2*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{3}(1)(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*2ln(lg(log_{1}^{x}))(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}log(1, x)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))*-3*0lg(x)}{x^{3}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))*-0lg(x)}{x^{3}log(1, x)ln^{3}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}log(1, x)ln^{3}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})ln{10}(x)} - \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}*-2*0ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{3}(1)(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{3}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-3*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{3}(1)(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*2lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})ln{10}(x)} - \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})ln(lg(log_{1}^{x}))lg(x)}{x^{3}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-3*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2*0lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{3}(1)(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{3}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})ln{10}(x)} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0}{x^{3}log(1, x)ln^{3}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-0ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}ln(1)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{-3{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{4}(ln(1))})lg^{3}(x)}{x^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{4}(1)(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3*0lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{3}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{4}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}*3lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})ln{10}(x)} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{4}(ln(1))})lg^{2}(x)}{x^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{4}(1)(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3*0lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg^{2}(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{4}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*2lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})ln{10}(x)} + \frac{2*-3{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{4}(ln(1))})lg(x)}{x^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-3*0lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{4}(1)(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-3*0lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})lg(x)}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{4}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}}{x^{3}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})ln{10}(x)} - \frac{6*-3{lg(log_{1}^{x})}^{lg(x)}}{x^{4}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{6({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))}{x^{3}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})}{x^{3}ln(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}*-0}{x^{3}log(1, x)ln^{2}(1)(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}*-2*0}{x^{3}log(1, x)ln(1)ln^{3}{10}lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})}{x^{3}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} + \frac{4*-3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{4({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))ln(lg(log_{1}^{x}))}{x^{3}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{2}(ln(1))})ln(lg(log_{1}^{x}))}{x^{3}ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)(lg(log_{1}^{x}))ln{10}(log_{1}^{x})ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-3*0}{x^{3}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-0}{x^{3}log(1, x)ln^{3}{10}ln^{2}(1)(1)lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}log(1, x)ln^{3}{10}ln(1)lg^{2}(log_{1}^{x})ln{10}(log_{1}^{x})} - \frac{3*-3{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3({lg(log_{1}^{x})}^{lg(x)}((\frac{1}{ln{10}(x)})ln(lg(log_{1}^{x})) + \frac{(lg(x))(\frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{ln{10}(log_{1}^{x})})}{(lg(log_{1}^{x}))}))}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{{\left(log(1, x)^{3}(ln(1))})}{x^{3}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2*0}{x^{3}{\left(log(1, x)^{2}ln^{3}(1)(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-3*0}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{1}^{x}}{(1)})}{(ln(1))})}{x^{3}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{3}(log_{1}^{x})ln{10}(log_{1}^{x})}\\=&\frac{-6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}ln{10}} + \frac{11{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{4}ln^{2}{10}} + \frac{11{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{24{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))}{x^{4}ln^{3}{10}} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{12{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{17{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{7{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} - \frac{14{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} - \frac{7{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}{10}ln^{3}(1)lg^{2}(log_{1}^{x})} - \frac{12{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{4}(lg(log_{1}^{x}))}{x^{4}ln^{4}{10}} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}{10}ln^{3}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg(log_{1}^{x})} - \frac{7{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} + \frac{5{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{11{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{2}{10}ln(1)lg(log_{1}^{x})} - \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{3}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln{10}lg(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}{10}ln^{2}(1)lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{11{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{2}{10}ln^{3}(1)lg(log_{1}^{x})} + \frac{11{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{11{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} + \frac{18{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}{10}ln^{3}(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}{10}ln^{3}(1)lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} - \frac{18{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}{10}ln^{3}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{3}(lg(log_{1}^{x}))lg(x)}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}log(1, x)ln(1)ln{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{18{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{12{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{11{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{12{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{11{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} + \frac{18{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{12{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{3}(log_{1}^{x})} - \frac{10{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg^{3}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{4}{10}lg^{4}(log_{1}^{x})} + \frac{11{lg(log_{1}^{x})}^{lg(x)}lg^{2}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{4}{10}lg^{4}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} + \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{3}(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg^{2}(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))lg(x)}{x^{4}{\left(log(1, x)^{3}ln^{4}{10}ln^{3}(1)lg^{3}(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} - \frac{24{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{3}{10}ln(1)lg(log_{1}^{x})} + \frac{9{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} - \frac{2{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} + \frac{{lg(log_{1}^{x})}^{lg(x)}lg^{4}(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{4}{10}lg^{4}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}lg(x)}{x^{4}{\left(log(1, x)^{4}ln^{4}(1)ln^{4}{10}lg^{4}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} + \frac{8{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{2{lg(log_{1}^{x})}^{lg(x)}ln^{2}(lg(log_{1}^{x}))}{x^{4}log(1, x)ln^{4}{10}ln(1)lg(log_{1}^{x})} + \frac{18{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} + \frac{3{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{22{lg(log_{1}^{x})}^{lg(x)}}{x^{4}log(1, x)ln(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{9{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{4}{10}lg^{2}(log_{1}^{x})} - \frac{6{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})} + \frac{18{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{2}{10}lg(log_{1}^{x})} + \frac{12{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{3}{10}lg^{2}(log_{1}^{x})} - \frac{{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg(log_{1}^{x})} + \frac{8{lg(log_{1}^{x})}^{lg(x)}}{x^{4}{\left(log(1, x)^{3}ln^{3}(1)ln^{4}{10}lg^{3}(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{3}{10}ln^{2}(1)lg(log_{1}^{x})} - \frac{4{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{2}(1)ln^{3}{10}lg(log_{1}^{x})} - \frac{3{lg(log_{1}^{x})}^{lg(x)}ln(lg(log_{1}^{x}))}{x^{4}{\left(log(1, x)^{2}ln^{4}{10}ln^{2}(1)lg^{2}(log_{1}^{x})}\\ \end{split}\end{equation} \]

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