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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{log_{a}^{x}}^{log_{b}^{x}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{log_{a}^{x}}^{log_{b}^{x}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})\\=&\frac{1}{xlog(b, x)ln(b)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{xlog(a, x)ln(a)ln(log_{a}^{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xlog(b, x)ln(b)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{xlog(a, x)ln(a)ln(log_{a}^{x})}\right)}{dx}\\=&\frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{xln(b)ln(log_{a}^{x})} + \frac{-0}{xlog(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} + \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{xlog(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{xln(a)ln(log_{a}^{x})} - \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{xlog(a, x)ln(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{xlog(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{xlog(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{1}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{1}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})}\right)}{dx}\\=&\frac{--2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}ln(b)ln(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} - \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{-2*0}{x^{2}{\left(log(b, x)^{2}ln^{3}(b)(b)ln(log_{a}^{x})} - \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{2}log(b, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)log(a, x)ln^{2}(b)(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} - \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{2}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{-0}{x^{2}log(b, x)log(a, x)ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)log(a, x)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} - \frac{-0}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln(a)ln(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{x^{2}log(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{3}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{1}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{1}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{2}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{3}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{1}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{1}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{2}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}ln(b)ln(log_{a}^{x})} + \frac{2*-0}{x^{3}log(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} + \frac{2*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{3*-3}{x^{4}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}ln^{2}(b)ln(log_{a}^{x})} + \frac{3*-2*0}{x^{3}{\left(log(b, x)^{2}ln^{3}(b)(b)ln(log_{a}^{x})} + \frac{3*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{3*-3}{x^{4}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}log(b, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln^{2}(b)(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} + \frac{3*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{4}(ln(b))})}{x^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2*-3*0}{x^{3}{\left(log(b, x)^{3}ln^{4}(b)(b)ln(log_{a}^{x})} + \frac{2*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{3}(b)(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} + \frac{2*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{3}(a)(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln^{2}(b)(b)ln^{2}(log_{a}^{x})} + \frac{2*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(b)(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{4}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)(a)} + \frac{3*-3}{x^{4}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)log(a, x)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{-3}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{-2*0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{3}(b)(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} + \frac{-0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(b)(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(a)(a)ln^{3}(log_{a}^{x})} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})} + \frac{-3}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{-0}{x^{3}log(b, x){\left(log(a, x)^{2}ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{-2*0}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{3}(a)(a)} + \frac{2*-3}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-0}{x^{3}log(b, x){\left(log(a, x)^{2}ln^{2}(b)(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{4}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{2*-2*0}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)(a)} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{2}(a)ln(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})}{x^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{5*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln(a)ln(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{x^{3}log(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})}{x^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})} - \frac{4*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{-6}{x^{4}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{11}{x^{4}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{11}{x^{4}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}{\left(log(b, x)^{4}ln^{4}(b)ln(log_{a}^{x})} - \frac{6}{x^{4}{\left(log(b, x)^{3}log(a, x)ln^{3}(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{3}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(a)ln^{2}(b)ln^{2}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln(b)ln^{2}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln^{3}(log_{a}^{x})ln(b)} - \frac{12}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln(b)ln^{3}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{12}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{3}(a)ln^{4}(log_{a}^{x})} - \frac{11}{x^{4}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{6}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{3}log(a, x)ln^{3}(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{2}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{6}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{4}(log_{a}^{x})ln^{3}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} - \frac{1}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})ln^{2}(a)} - \frac{2}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{12}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)} - \frac{2}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{2}(log_{a}^{x})ln^{3}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{4}(log_{a}^{x})ln^{3}(a)} + \frac{30log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{3}(log_{a}^{x})} + \frac{20log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{2}(log_{a}^{x})} + \frac{30log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{3}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{12log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} + \frac{24log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln(log_{a}^{x})} + \frac{12log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} + \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{2}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{4}(log_{a}^{x})} + \frac{18log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{4}(log_{a}^{x})}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{log_{a}^{x}}^{log_{b}^{x}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{log_{a}^{x}}^{log_{b}^{x}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})\\=&\frac{1}{xlog(b, x)ln(b)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{xlog(a, x)ln(a)ln(log_{a}^{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xlog(b, x)ln(b)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{xlog(a, x)ln(a)ln(log_{a}^{x})}\right)}{dx}\\=&\frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{xln(b)ln(log_{a}^{x})} + \frac{-0}{xlog(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} + \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{xlog(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{xln(a)ln(log_{a}^{x})} - \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{xlog(a, x)ln(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{xlog(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{xlog(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{1}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{1}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{1}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})}\right)}{dx}\\=&\frac{--2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}ln(b)ln(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} - \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{-2*0}{x^{2}{\left(log(b, x)^{2}ln^{3}(b)(b)ln(log_{a}^{x})} - \frac{-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{2}log(b, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)log(a, x)ln^{2}(b)(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{-0}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} - \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)log(a, x)ln(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{-2}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{2}log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{2}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{-0}{x^{2}log(b, x)log(a, x)ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(b, x)log(a, x)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} - \frac{-0}{x^{2}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln(a)ln(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{x^{2}log(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}log(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{-2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{2}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} + \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{2}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{3}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{1}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{1}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{2}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{3}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{3}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{1}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{2}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{1}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{2}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})}\right)}{dx}\\=&\frac{2*-3}{x^{4}log(b, x)ln(b)ln(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}ln(b)ln(log_{a}^{x})} + \frac{2*-0}{x^{3}log(b, x)ln^{2}(b)(b)ln(log_{a}^{x})} + \frac{2*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{3*-3}{x^{4}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} + \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}ln^{2}(b)ln(log_{a}^{x})} + \frac{3*-2*0}{x^{3}{\left(log(b, x)^{2}ln^{3}(b)(b)ln(log_{a}^{x})} + \frac{3*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{3*-3}{x^{4}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}log(b, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln^{2}(b)(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} + \frac{3*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)log(a, x)ln(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{4}(ln(b))})}{x^{3}ln^{3}(b)ln(log_{a}^{x})} + \frac{2*-3*0}{x^{3}{\left(log(b, x)^{3}ln^{4}(b)(b)ln(log_{a}^{x})} + \frac{2*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{3}ln^{3}(b)ln^{2}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{3}(b)(b)ln(a)ln^{2}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(a)(a)ln^{2}(log_{a}^{x})} + \frac{2*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{3}(a)(a)ln(b)ln^{2}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln^{2}(b)(b)ln^{2}(log_{a}^{x})} + \frac{2*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(b)(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{4}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)(a)} + \frac{3*-3}{x^{4}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{3*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x)log(a, x)ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} + \frac{3*-0}{x^{3}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{-3}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{3}(ln(b))})}{x^{3}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})}{x^{3}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{-2*0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{3}(b)(b)ln^{2}(log_{a}^{x})ln(a)} + \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln(a)} + \frac{-0}{x^{3}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln^{2}(a)(a)} + \frac{2*-3}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2*-0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln^{2}(b)(b)ln^{2}(a)ln^{3}(log_{a}^{x})} + \frac{2*-2*0}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(a)(a)ln^{3}(log_{a}^{x})} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})} + \frac{-3}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{-0}{x^{3}log(b, x){\left(log(a, x)^{2}ln^{2}(b)(b)ln^{2}(log_{a}^{x})ln^{2}(a)} + \frac{-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{-2*0}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{3}(a)(a)} + \frac{2*-3}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{{\left(log(b, x)^{2}(ln(b))})}{x^{3}{\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-0}{x^{3}log(b, x){\left(log(a, x)^{2}ln^{2}(b)(b)ln^{3}(log_{a}^{x})ln^{2}(a)} + \frac{2*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{4}(log_{a}^{x})(log_{a}^{x})ln^{2}(a)} + \frac{2*-2*0}{x^{3}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)(a)} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{2}(a)ln(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})}{x^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{2}(log_{a}^{x})} - \frac{log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{5*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{2}(log_{a}^{x})} - \frac{5log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{2(\frac{-(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{2}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln(a)ln(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}log(a, x)ln(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-0}{x^{3}log(a, x)ln^{2}(a)(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}log(a, x)ln(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})}{x^{3}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{3*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{3}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2*0}{x^{3}{\left(log(a, x)^{2}ln^{3}(a)(a)ln^{2}(log_{a}^{x})} - \frac{3log_{log_{a}^{x}}^{log_{b}^{x}}*-2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{2}ln^{2}(a)ln^{3}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})(log_{a}^{x})} - \frac{2*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})}{x^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{3}(log_{a}^{x})} - \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})} - \frac{4*-3log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{{\left(log(a, x)^{4}(ln(a))})log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4(\frac{(\frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{b}^{x}}{(b)})}{(ln(b))}))}{(log_{b}^{x})} - \frac{((\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))}))log_{log_{a}^{x}}^{log_{b}^{x}}}{(log_{a}^{x})})}{(ln(log_{a}^{x}))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}*-3*0}{x^{3}{\left(log(a, x)^{3}ln^{4}(a)(a)ln^{3}(log_{a}^{x})} - \frac{4log_{log_{a}^{x}}^{log_{b}^{x}}*-3(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{a}^{x}}{(a)})}{(ln(a))})}{x^{3}{\left(log(a, x)^{3}ln^{3}(a)ln^{4}(log_{a}^{x})(log_{a}^{x})}\\=&\frac{-6}{x^{4}log(b, x)ln(b)ln(log_{a}^{x})} - \frac{11}{x^{4}{\left(log(b, x)^{2}ln^{2}(b)ln(log_{a}^{x})} - \frac{11}{x^{4}log(b, x)log(a, x)ln(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(b, x)^{3}ln^{3}(b)ln(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln^{2}(a)ln(b)ln^{2}(log_{a}^{x})} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}{\left(log(b, x)^{4}ln^{4}(b)ln(log_{a}^{x})} - \frac{6}{x^{4}{\left(log(b, x)^{3}log(a, x)ln^{3}(b)ln(a)ln^{2}(log_{a}^{x})} - \frac{3}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(a)ln^{2}(b)ln^{2}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln(b)ln^{2}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(a)ln^{2}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln^{3}(log_{a}^{x})ln(b)} - \frac{12}{x^{4}{\left(log(a, x)^{3}log(b, x)ln^{3}(a)ln(b)ln^{3}(log_{a}^{x})} - \frac{4}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{12}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{3}(a)ln^{4}(log_{a}^{x})} - \frac{11}{x^{4}log(b, x)log(a, x)ln(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{6}{x^{4}{\left(log(b, x)^{2}log(a, x)ln^{2}(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{12}{x^{4}{\left(log(a, x)^{2}log(b, x)ln(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{3}log(a, x)ln^{3}(b)ln^{2}(log_{a}^{x})ln(a)} - \frac{2}{x^{4}{\left(log(a, x)^{2}{\left(log(b, x)^{2}ln^{2}(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{2}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(a)ln^{3}(log_{a}^{x})} - \frac{6}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{4}(log_{a}^{x})ln^{3}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{2}(log_{a}^{x})ln^{2}(a)} - \frac{1}{x^{4}{\left(log(b, x)^{2}{\left(log(a, x)^{2}ln^{2}(b)ln^{2}(log_{a}^{x})ln^{2}(a)} - \frac{2}{x^{4}{\left(log(a, x)^{3}log(b, x)ln(b)ln^{3}(a)ln^{3}(log_{a}^{x})} - \frac{12}{x^{4}log(b, x){\left(log(a, x)^{2}ln(b)ln^{3}(log_{a}^{x})ln^{2}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{3}(log_{a}^{x})ln^{3}(a)} - \frac{2}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{2}(log_{a}^{x})ln^{3}(a)} - \frac{6}{x^{4}log(b, x){\left(log(a, x)^{3}ln(b)ln^{4}(log_{a}^{x})ln^{3}(a)} + \frac{30log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{3}(log_{a}^{x})} + \frac{20log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{2}(log_{a}^{x})} + \frac{30log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{3}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}log(a, x)ln(a)ln(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{11log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{2}ln^{2}(a)ln^{2}(log_{a}^{x})} + \frac{12log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} + \frac{24log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{3}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln(log_{a}^{x})} + \frac{12log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln(log_{a}^{x})} + \frac{2log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{2}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{3}ln^{3}(a)ln^{2}(log_{a}^{x})} + \frac{6log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{4}(log_{a}^{x})} + \frac{18log_{log_{a}^{x}}^{log_{b}^{x}}}{x^{4}{\left(log(a, x)^{4}ln^{4}(a)ln^{4}(log_{a}^{x})}\\ \end{split}\end{equation} \]
你的问题在这里没有得到解决？请到 热门难题 里面看看吧！
最 新 发 布
新增加身体健康评估计算器，位置：“数学运算 > 身体健康评估”。
新增加学习笔记(安卓版)百度网盘快速下载应用程序，欢迎使用。
新增加学习笔记(安卓版)本站下载应用程序，欢迎使用。
新增线性代数行列式的计算，欢迎使用。
数学计算和一元方程已经支持正割函数和余割函数，欢迎使用。
新增加贷款计算器模块（具体位置：数学运算 > 贷款计算器），欢迎使用。