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。
\[ \begin{equation}\begin{split}【1/1】求函数{{x}^{x}}^{ln(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {{x}^{x}}^{ln(x)}\right)}{dx}\\=&({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))\\=&\frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x) + {{x}^{x}}^{ln(x)}ln(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x) + {{x}^{x}}^{ln(x)}ln(x)\right)}{dx}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x) + \frac{{{x}^{x}}^{ln(x)}*2ln(x)}{(x)} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x) + \frac{{{x}^{x}}^{ln(x)}}{(x)}\\=&\frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x} + \frac{3{{x}^{x}}^{ln(x)}ln(x)}{x} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{4}(x) + 2{{x}^{x}}^{ln(x)}ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x} + \frac{3{{x}^{x}}^{ln(x)}ln(x)}{x} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{4}(x) + 2{{x}^{x}}^{ln(x)}ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x)\right)}{dx}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x(x)} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x(x)} + \frac{-{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x(x)} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x(x)} + \frac{{{x}^{x}}^{ln(x)}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{3*-{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}}{x(x)} - \frac{-2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} - \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{2}} - \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x) + \frac{{{x}^{x}}^{ln(x)}*4ln^{3}(x)}{(x)} + 2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{(x)} + \frac{2*-{{x}^{x}}^{ln(x)}}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{x} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x) + \frac{{{x}^{x}}^{ln(x)}*2ln(x)}{(x)}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} - \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} - \frac{4{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{6}(x) + 3{{x}^{x}}^{ln(x)}ln^{5}(x) + 3{{x}^{x}}^{ln(x)}ln^{4}(x) + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} - \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} - \frac{4{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{6}(x) + 3{{x}^{x}}^{ln(x)}ln^{5}(x) + 3{{x}^{x}}^{ln(x)}ln^{4}(x) + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{3}(x)\right)}{dx}\\=&\frac{--2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{3}} - \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x^{2}} - \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x^{2}({x}^{x})} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x^{2}(x)} + \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})*2ln(x)}{x^{2}(x)} + \frac{2*-{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}*4ln^{3}(x)ln({x}^{x})}{x(x)} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{4*-{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x^{2}} + \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}*3ln^{2}(x)ln({x}^{x})}{x(x)} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{4*-2{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{3}} + \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln({x}^{x})}{x^{2}} + \frac{4{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}(x)} + \frac{4{{x}^{x}}^{ln(x)}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{2*-{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x(x)} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{2*-2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}(x)} + \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}(x)} - \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{3}} - \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x^{2}(x)} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-2{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}*2ln(x)ln^{2}({x}^{x})}{x^{2}(x)} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{4}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{4}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*4ln^{3}(x)}{x(x)} + \frac{2*-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{3}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{3}(x)}{x({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})*3ln^{2}(x)}{x(x)} + \frac{-2{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}(x)} + \frac{{{x}^{x}}^{ln(x)}ln(x)*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x(x)} + \frac{9*-{{x}^{x}}^{ln(x)}ln^{3}(x)}{x^{2}} + \frac{9({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{x(x)} - \frac{3*-3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{4}} - \frac{3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})}{x^{3}} - \frac{3{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + \frac{6*-{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{6({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x} + \frac{6{{x}^{x}}^{ln(x)}}{x(x)} + \frac{15*-{{x}^{x}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{15({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}*2ln(x)}{x(x)} - \frac{4*-2{{x}^{x}}^{ln(x)}ln(x)}{x^{3}} - \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x^{2}} - \frac{4{{x}^{x}}^{ln(x)}}{x^{2}(x)} + \frac{-3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{4}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}({x}^{x})}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}*3ln^{2}({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + \frac{6*-2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + \frac{6({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{2}} + \frac{6{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{6}(x) + \frac{{{x}^{x}}^{ln(x)}*6ln^{5}(x)}{(x)} + 3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{5}(x) + \frac{3{{x}^{x}}^{ln(x)}*5ln^{4}(x)}{(x)} + 3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x) + \frac{3{{x}^{x}}^{ln(x)}*4ln^{3}(x)}{(x)} + \frac{2*-3{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{4}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{3}} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x) + \frac{{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{(x)}\\=&\frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{3}} - \frac{7{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{3}} - \frac{5{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{4}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{17{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x^{2}} + \frac{34{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} - \frac{18{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})ln^{2}(x)}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{6}(x)ln({x}^{x})}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{5}(x)ln({x}^{x})}{x} + \frac{20{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{4}(x)}{x^{2}} + \frac{9{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{6{{x}^{x}}^{ln(x)}ln^{3}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{12{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{6{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{3}(x)}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} - \frac{5{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} - \frac{8{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})ln(x)}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{3}({x}^{x})}{x^{3}} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x^{2}} + \frac{7{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{6}(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{5}(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{11{{x}^{x}}^{ln(x)}ln^{2}(x)}{x^{2}} - \frac{6{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{4}} + \frac{42{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} + \frac{48{{x}^{x}}^{ln(x)}ln^{4}(x)}{x} + \frac{36{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} - \frac{12{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} - \frac{16{{x}^{x}}^{ln(x)}ln^{3}(x)}{x^{2}} + \frac{18{{x}^{x}}^{ln(x)}ln^{5}(x)}{x} + \frac{10{{x}^{x}}^{ln(x)}ln(x)}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{4}({x}^{x})}{x^{4}} + {{x}^{x}}^{ln(x)}ln^{8}(x) + 4{{x}^{x}}^{ln(x)}ln^{7}(x) + 6{{x}^{x}}^{ln(x)}ln^{6}(x) + 4{{x}^{x}}^{ln(x)}ln^{5}(x) - \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{4}} + \frac{11{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{4}} + \frac{12{{x}^{x}}^{ln(x)}}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{4}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{{x}^{x}}^{ln(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {{x}^{x}}^{ln(x)}\right)}{dx}\\=&({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))\\=&\frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x) + {{x}^{x}}^{ln(x)}ln(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x) + {{x}^{x}}^{ln(x)}ln(x)\right)}{dx}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x) + \frac{{{x}^{x}}^{ln(x)}*2ln(x)}{(x)} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x) + \frac{{{x}^{x}}^{ln(x)}}{(x)}\\=&\frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x} + \frac{3{{x}^{x}}^{ln(x)}ln(x)}{x} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{4}(x) + 2{{x}^{x}}^{ln(x)}ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x} + \frac{3{{x}^{x}}^{ln(x)}ln(x)}{x} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{4}(x) + 2{{x}^{x}}^{ln(x)}ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}}{x} + {{x}^{x}}^{ln(x)}ln^{2}(x)\right)}{dx}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x(x)} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x(x)} + \frac{-{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x(x)} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln({x}^{x})}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})}{x(x)} + \frac{{{x}^{x}}^{ln(x)}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{3*-{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}}{x(x)} - \frac{-2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} - \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{2}} - \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x) + \frac{{{x}^{x}}^{ln(x)}*4ln^{3}(x)}{(x)} + 2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x) + \frac{2{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{(x)} + \frac{2*-{{x}^{x}}^{ln(x)}}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))}{x} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x) + \frac{{{x}^{x}}^{ln(x)}*2ln(x)}{(x)}\\=&\frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} - \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} - \frac{4{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{6}(x) + 3{{x}^{x}}^{ln(x)}ln^{5}(x) + 3{{x}^{x}}^{ln(x)}ln^{4}(x) + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} - \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} - \frac{4{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}} + {{x}^{x}}^{ln(x)}ln^{6}(x) + 3{{x}^{x}}^{ln(x)}ln^{5}(x) + 3{{x}^{x}}^{ln(x)}ln^{4}(x) + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{3}(x)\right)}{dx}\\=&\frac{--2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{3}} - \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x^{2}} - \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x^{2}({x}^{x})} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x^{2}(x)} + \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})*2ln(x)}{x^{2}(x)} + \frac{2*-{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}*4ln^{3}(x)ln({x}^{x})}{x(x)} + \frac{2{{x}^{x}}^{ln(x)}ln^{4}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{4*-{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x^{2}} + \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x)ln({x}^{x})}{x} + \frac{4{{x}^{x}}^{ln(x)}*3ln^{2}(x)ln({x}^{x})}{x(x)} + \frac{4{{x}^{x}}^{ln(x)}ln^{3}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{4*-2{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{3}} + \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln({x}^{x})}{x^{2}} + \frac{4{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}(x)} + \frac{4{{x}^{x}}^{ln(x)}ln(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{2*-{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x} + \frac{2{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x(x)} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x({x}^{x})} + \frac{2*-2{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{2}(x)} + \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{3}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})ln(x)}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}(x)} - \frac{2*-2{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{3}} - \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln({x}^{x})}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}*2ln(x)ln({x}^{x})}{x^{2}(x)} - \frac{2{{x}^{x}}^{ln(x)}ln^{2}(x)({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-2{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}*2ln(x)ln^{2}({x}^{x})}{x^{2}(x)} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{4}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{4}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*4ln^{3}(x)}{x(x)} + \frac{2*-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x^{2}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{3}(x)}{x} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{3}(x)}{x({x}^{x})} + \frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})*3ln^{2}(x)}{x(x)} + \frac{-2{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{3}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)ln^{2}({x}^{x})}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{2}(x)} + \frac{{{x}^{x}}^{ln(x)}ln(x)*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + \frac{-{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x({x}^{x})} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})*2ln(x)}{x(x)} + \frac{9*-{{x}^{x}}^{ln(x)}ln^{3}(x)}{x^{2}} + \frac{9({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x)}{x} + \frac{9{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{x(x)} - \frac{3*-3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{4}} - \frac{3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}({x}^{x})}{x^{3}} - \frac{3{{x}^{x}}^{ln(x)}*2ln({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + \frac{6*-{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} + \frac{6({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x} + \frac{6{{x}^{x}}^{ln(x)}}{x(x)} + \frac{15*-{{x}^{x}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{15({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{2}(x)}{x} + \frac{15{{x}^{x}}^{ln(x)}*2ln(x)}{x(x)} - \frac{4*-2{{x}^{x}}^{ln(x)}ln(x)}{x^{3}} - \frac{4({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln(x)}{x^{2}} - \frac{4{{x}^{x}}^{ln(x)}}{x^{2}(x)} + \frac{-3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{4}} + \frac{({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}({x}^{x})}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}*3ln^{2}({x}^{x})({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + \frac{6*-2{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + \frac{6({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{2}} + \frac{6{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{6}(x) + \frac{{{x}^{x}}^{ln(x)}*6ln^{5}(x)}{(x)} + 3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{5}(x) + \frac{3{{x}^{x}}^{ln(x)}*5ln^{4}(x)}{(x)} + 3({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{4}(x) + \frac{3{{x}^{x}}^{ln(x)}*4ln^{3}(x)}{(x)} + \frac{2*-3{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{4}} + \frac{2({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln({x}^{x})}{x^{3}} + \frac{2{{x}^{x}}^{ln(x)}({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}({x}^{x})} + ({{x}^{x}}^{ln(x)}((\frac{1}{(x)})ln({x}^{x}) + \frac{(ln(x))(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})}))ln^{3}(x) + \frac{{{x}^{x}}^{ln(x)}*3ln^{2}(x)}{(x)}\\=&\frac{2{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{3}} - \frac{7{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{3}} - \frac{5{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{4}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{17{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x^{2}} + \frac{34{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{2}} - \frac{18{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})ln^{2}(x)}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{6}(x)ln({x}^{x})}{x} + \frac{9{{x}^{x}}^{ln(x)}ln^{5}(x)ln({x}^{x})}{x} + \frac{20{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{2}(x)}{x^{2}} + \frac{4{{x}^{x}}^{ln(x)}ln(x)ln^{2}({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{4}(x)}{x^{2}} + \frac{9{{x}^{x}}^{ln(x)}ln^{4}(x)ln({x}^{x})}{x} + \frac{6{{x}^{x}}^{ln(x)}ln^{3}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{12{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{2}} + \frac{6{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{3}(x)}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{2}} + \frac{2{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln(x)}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln(x)ln({x}^{x})}{x^{2}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}(x)ln({x}^{x})}{x} - \frac{5{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{2}({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})ln^{2}(x)}{x^{2}} - \frac{8{{x}^{x}}^{ln(x)}ln({x}^{x})ln(x)}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}ln^{2}(x)ln^{3}({x}^{x})}{x^{3}} + \frac{6{{x}^{x}}^{ln(x)}ln^{2}(x)ln({x}^{x})}{x^{3}} + \frac{3{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})ln(x)}{x^{3}} + \frac{{{x}^{x}}^{ln(x)}ln(x)ln^{3}({x}^{x})}{x^{3}} - \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x^{2}} + \frac{7{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x^{2}} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{6}(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{5}(x)}{x} + \frac{3{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{4}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln({x}^{x})ln^{3}(x)}{x} + \frac{11{{x}^{x}}^{ln(x)}ln^{2}(x)}{x^{2}} - \frac{6{{x}^{x}}^{ln(x)}ln^{3}({x}^{x})}{x^{4}} + \frac{42{{x}^{x}}^{ln(x)}ln^{3}(x)}{x} + \frac{48{{x}^{x}}^{ln(x)}ln^{4}(x)}{x} + \frac{36{{x}^{x}}^{ln(x)}ln(x)}{x^{2}} - \frac{12{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{3}} - \frac{16{{x}^{x}}^{ln(x)}ln^{3}(x)}{x^{2}} + \frac{18{{x}^{x}}^{ln(x)}ln^{5}(x)}{x} + \frac{10{{x}^{x}}^{ln(x)}ln(x)}{x^{3}} + \frac{12{{x}^{x}}^{ln(x)}ln^{2}(x)}{x} + \frac{{{x}^{x}}^{ln(x)}ln^{4}({x}^{x})}{x^{4}} + {{x}^{x}}^{ln(x)}ln^{8}(x) + 4{{x}^{x}}^{ln(x)}ln^{7}(x) + 6{{x}^{x}}^{ln(x)}ln^{6}(x) + 4{{x}^{x}}^{ln(x)}ln^{5}(x) - \frac{6{{x}^{x}}^{ln(x)}ln({x}^{x})}{x^{4}} + \frac{11{{x}^{x}}^{ln(x)}ln^{2}({x}^{x})}{x^{4}} + \frac{12{{x}^{x}}^{ln(x)}}{x^{2}} - \frac{2{{x}^{x}}^{ln(x)}}{x^{3}} + {{x}^{x}}^{ln(x)}ln^{4}(x)\\ \end{split}\end{equation} \]
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