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。
\[ \begin{equation}\begin{split}【1/1】求函数{(1 - x)}^{x}{\frac{1}{x}}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (-x + 1)^{x}{\frac{1}{x}}^{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (-x + 1)^{x}{\frac{1}{x}}^{x}\right)}{dx}\\=&((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x} + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))\\=&(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} + {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - {\frac{1}{x}}^{x}(-x + 1)^{x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} + {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - {\frac{1}{x}}^{x}(-x + 1)^{x}\right)}{dx}\\=&((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)} - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)} + ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x}) + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x}) + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(\frac{1}{x})x^{2}} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x} - {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))\\=&{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) - 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - {\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{x} - (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) + {\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) - 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - {\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{x} - (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) + {\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)}\right)}{dx}\\=&({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})ln(-x + 1) + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*-ln(-x + 1)}{(\frac{1}{x})x^{2}} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})(-1 + 0)}{(-x + 1)} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{2x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{2x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{(-x + 1)} - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)(-x + 1)} + ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)ln(\frac{1}{x}) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)ln(\frac{1}{x})}{(-x + 1)} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)*-1}{(\frac{1}{x})x^{2}} + ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{2}(\frac{1}{x}) + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{2}(\frac{1}{x}) + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*2ln(\frac{1}{x})*-1}{(\frac{1}{x})x^{2}} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)} - \frac{2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)} - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{(-x + 1)} - \frac{x{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} + ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{2}(-x + 1) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(-x + 1) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}*2ln(-x + 1)(-1 + 0)}{(-x + 1)} - 2({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x}) - 2{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x}) - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(\frac{1}{x})x^{2}} - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x}) - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} - (\frac{-2(-1 + 0)}{(-x + 1)^{3}})x(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{2}} + (\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x} + \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{x^{2}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{x^{2}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{2}} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1) - {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1) - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)}{(-x + 1)} + (\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} + \frac{x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{(-x + 1)} + \frac{x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{(-x + 1)} - \frac{-(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{2}} - \frac{((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{x} - \frac{(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x} - ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1) - (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1) - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)} + ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x} + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})) + (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} + \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)} + \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)}\\=&2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})ln(-x + 1) + 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)ln(\frac{1}{x}) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{x} - \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x}) - \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{x} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln^{2}(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln^{2}(-x + 1) - 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{x} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{5{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{4x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} + \frac{2x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} + {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(\frac{1}{x}) - 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) + (-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(-x + 1) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1) + \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{x} + \frac{x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{4x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{7x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} - \frac{x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} + 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{2x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{2}} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}}{x} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})ln(-x + 1) + 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)ln(\frac{1}{x}) - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{x} - \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x}) - \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{x} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln^{2}(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln^{2}(-x + 1) - 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{x} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{5{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{4x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} + \frac{2x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} + {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(\frac{1}{x}) - 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) + (-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(-x + 1) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - 2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1) + \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{x} + \frac{x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{4x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{7x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} - \frac{x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} + 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{2x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{2}} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}}{x} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - {\frac{1}{x}}^{x}(-x + 1)^{x} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)}\right)}{dx}\\=&2({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{2}(\frac{1}{x})ln(-x + 1) + 2{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{2}(\frac{1}{x})ln(-x + 1) + \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}*2ln(\frac{1}{x})*-ln(-x + 1)}{(\frac{1}{x})x^{2}} + \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})(-1 + 0)}{(-x + 1)} + 2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{2}(-x + 1)ln(\frac{1}{x}) + 2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(-x + 1)ln(\frac{1}{x}) + \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}*2ln(-x + 1)(-1 + 0)ln(\frac{1}{x})}{(-x + 1)} + \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)*-1}{(\frac{1}{x})x^{2}} - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1) - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}*-ln(-x + 1)}{(-x + 1)(\frac{1}{x})x^{2}} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})(-1 + 0)}{(-x + 1)(-x + 1)} - \frac{2*-(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{x^{2}} - \frac{2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{x} - \frac{2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{x} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{x(-x + 1)} - 4(\frac{-(-1 + 0)}{(-x + 1)^{2}}){\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{4({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{4{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{(-x + 1)} - \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} - 3(\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{3x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{3x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)ln(\frac{1}{x})}{(-x + 1)(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)*-1}{(-x + 1)(\frac{1}{x})x^{2}} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}*-ln(-x + 1)}{(-x + 1)(\frac{1}{x})x^{2}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})(-1 + 0)}{(-x + 1)(-x + 1)} - 3(\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} - \frac{3x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} - \frac{3x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(-x + 1)}{(-x + 1)} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}*2ln(-x + 1)(-1 + 0)}{(-x + 1)(-x + 1)} + 3(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) + \frac{3*2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} + \frac{3x^{2}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} + \frac{3x^{2}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{(-x + 1)^{2}} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)^{2}(-x + 1)} - 3(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{3x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{3x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{(-x + 1)^{2}} - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)^{2}(-x + 1)} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}*2ln(\frac{1}{x})*-1}{(-x + 1)(\frac{1}{x})x^{2}} - 2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(-x + 1)^{2}(\frac{1}{x})x^{2}} - 3({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) - 3{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})ln(-x + 1) - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}*-ln(-x + 1)}{(\frac{1}{x})x^{2}} - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})(-1 + 0)}{(-x + 1)} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x}) - {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1)ln(\frac{1}{x}) - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)ln(\frac{1}{x})}{(-x + 1)} - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)*-1}{(\frac{1}{x})x^{2}} - 4(\frac{-(-1 + 0)}{(-x + 1)^{2}})(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) - \frac{4((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{4(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{(-x + 1)} - \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)(-x + 1)} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x}) - \frac{2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} - \frac{-{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{x^{2}} - \frac{({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1)}{x} - \frac{{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1)}{x} - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)}{x(-x + 1)} + ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)ln^{2}(\frac{1}{x}) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)ln^{2}(\frac{1}{x}) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)ln^{2}(\frac{1}{x})}{(-x + 1)} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)*2ln(\frac{1}{x})*-1}{(\frac{1}{x})x^{2}} + ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})ln^{2}(-x + 1) + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})ln^{2}(-x + 1) + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*-ln^{2}(-x + 1)}{(\frac{1}{x})x^{2}} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})*2ln(-x + 1)(-1 + 0)}{(-x + 1)} - 2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) - 2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)ln(\frac{1}{x}) - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)ln(\frac{1}{x})}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)*-1}{(\frac{1}{x})x^{2}} - \frac{3*-{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{x^{2}} - \frac{3({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{x} - \frac{3{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{x} - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{x(\frac{1}{x})x^{2}} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}}){\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) - \frac{2({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} - \frac{2{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1)}{(-x + 1)} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)}{(-x + 1)(-x + 1)} + 5(\frac{-(-1 + 0)}{(-x + 1)^{2}}){\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{5({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{(-x + 1)} + \frac{5{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{(-x + 1)} - (\frac{-2(-1 + 0)}{(-x + 1)^{3}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x}) - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}*-1}{(-x + 1)^{2}(\frac{1}{x})x^{2}} + 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1)}{(-x + 1)} + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)}{(-x + 1)(-x + 1)} + 4(\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) + \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{4x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{4x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{(-x + 1)} + \frac{4x{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x}) - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}*2ln(\frac{1}{x})*-1}{(-x + 1)(\frac{1}{x})x^{2}} + 2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x}) + \frac{2*2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{2x^{2}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{2x^{2}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{2x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}*-1}{(-x + 1)^{2}(\frac{1}{x})x^{2}} + 4(\frac{-(-1 + 0)}{(-x + 1)^{2}})(-x + 1)^{x}{\frac{1}{x}}^{x} + \frac{4((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)} + \frac{4(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)} + ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{3}(\frac{1}{x}) + {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{3}(\frac{1}{x}) + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*3ln^{2}(\frac{1}{x})*-1}{(\frac{1}{x})x^{2}} - 3({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{2}(\frac{1}{x}) - 3{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{2}(\frac{1}{x}) - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}*2ln(\frac{1}{x})*-1}{(\frac{1}{x})x^{2}} + ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{3}(-x + 1) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{3}(-x + 1) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}*3ln^{2}(-x + 1)(-1 + 0)}{(-x + 1)} - 3(\frac{-2(-1 + 0)}{(-x + 1)^{3}})(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{3((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{3(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{2}} - 2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln^{2}(-x + 1) - 2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(-x + 1) - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}*2ln(-x + 1)(-1 + 0)}{(-x + 1)} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln^{2}(-x + 1) - {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln^{2}(-x + 1) - \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}*2ln(-x + 1)(-1 + 0)}{(-x + 1)} + 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x}) + \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{2x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{2x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{(-x + 1)} + \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}*-1}{(-x + 1)(\frac{1}{x})x^{2}} + \frac{2*-(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{2}} + \frac{2((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{x} + \frac{2(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x} + (\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) + \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{x^{2}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{x^{2}{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(-x + 1)^{2}(\frac{1}{x})x^{2}} + 4(\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) + \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + \frac{4x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} + \frac{4x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1)}{(-x + 1)} + \frac{4x(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)(-x + 1)} + 2({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(-x + 1) + 2{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(-x + 1) + \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}(-1 + 0)}{(-x + 1)} + 3(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x} + \frac{3*2x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{3x^{2}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{3x^{2}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{3}} + 7(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x(-x + 1)^{x}{\frac{1}{x}}^{x} + \frac{7(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{7x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{2}} + \frac{7x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{2}} - (\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{x^{3}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{x^{3}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{3}} + 2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x{\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} + \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{(-x + 1)^{2}} + \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{(-x + 1)^{2}} - (\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x} - \frac{2x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} - \frac{x^{2}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{(-x + 1)^{2}} - \frac{x^{2}{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{(-x + 1)^{2}} + 3({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}ln(\frac{1}{x}) + 3{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))ln(\frac{1}{x}) + \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}*-1}{(\frac{1}{x})x^{2}} - 2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{2x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{2x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{3}} - 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x{\frac{1}{x}}^{x}(-x + 1)^{x} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{2x({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{(-x + 1)} - \frac{2x{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{(-x + 1)} - 2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{2*2x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{2x^{2}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{2x^{2}(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)^{2}} + \frac{-2(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{3}} + \frac{((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{x^{2}} + \frac{(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x^{2}} + \frac{-{\frac{1}{x}}^{x}(-x + 1)^{x}}{x^{2}} + \frac{({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x}}{x} + \frac{{\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)}))}{x} + ((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}ln(-x + 1) + (-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(-x + 1) + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}(-1 + 0)}{(-x + 1)} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))(-x + 1)^{x} - {\frac{1}{x}}^{x}((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})) - (\frac{-(-1 + 0)}{(-x + 1)^{2}})x(-x + 1)^{x}{\frac{1}{x}}^{x} - \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x((-x + 1)^{x}((1)ln(-x + 1) + \frac{(x)(-1 + 0)}{(-x + 1)})){\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x(-x + 1)^{x}({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{(-x + 1)}\\=&3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(\frac{1}{x})ln(-x + 1) + 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)ln^{2}(\frac{1}{x}) + 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(-x + 1)ln(\frac{1}{x}) - \frac{8x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{7{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{x} - \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} + 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})ln^{2}(-x + 1) - \frac{6x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - 8{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})ln(-x + 1) - 6(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)ln(\frac{1}{x}) - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{x} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)^{2}} - \frac{9(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)^{2}} + \frac{9x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{8{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} - \frac{6x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{x} - \frac{4(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{x} + \frac{20(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{6{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{x} - \frac{5x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)^{2}} - \frac{10{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{9(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})ln(-x + 1)}{(-x + 1)} + \frac{6x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{3x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{3x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln^{2}(-x + 1)}{(-x + 1)} + \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)} + \frac{3x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1)}{(-x + 1)^{2}} - \frac{4x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln^{2}(\frac{1}{x})}{(-x + 1)} + \frac{16{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} + \frac{9x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x})}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})ln^{2}(-x + 1)}{(-x + 1)} + \frac{16x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{6x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)^{2}} + \frac{11x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)^{2}} + \frac{12x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{3}} + \frac{25x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{4x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{3}} - \frac{8x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{3}} - \frac{6x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} - \frac{3x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(\frac{1}{x})}{(-x + 1)} - \frac{5x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)^{2}} - \frac{2x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} + \frac{20x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{6x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)^{2}} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)^{2}} + \frac{7x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} + \frac{27{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{4x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(-x + 1)}{(-x + 1)} + \frac{3x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)^{2}} - \frac{3x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)^{2}} + \frac{9x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1)}{(-x + 1)} - \frac{10(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - 2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1)ln(\frac{1}{x}) - {\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln^{2}(\frac{1}{x}) + \frac{7(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{x} + 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)ln(\frac{1}{x}) - 4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln^{2}(-x + 1) + 6{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln(-x + 1) + \frac{5x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{9{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} + \frac{9x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} + \frac{{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{x^{2}} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1)}{x} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)^{2}} + \frac{9(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + \frac{5{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{x} + \frac{4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{x^{2}} + \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{x^{2}} + \frac{12{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{x} - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1)}{(-x + 1)} + \frac{13{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} + \frac{17(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{15{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} - \frac{9x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)^{2}} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)^{2}} + \frac{3x{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1)}{(-x + 1)} - \frac{9x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)} - \frac{6x{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1)}{(-x + 1)} - \frac{6x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{3x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} - \frac{6x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{2}} - \frac{9(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)} - \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(\frac{1}{x})}{(-x + 1)} + \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})}{(-x + 1)} - \frac{6x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)}{(-x + 1)} - \frac{x^{3}{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})}{(-x + 1)^{3}} + (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln^{3}(\frac{1}{x}) - 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln^{2}(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x})ln^{3}(-x + 1) - \frac{3x(-x + 1)^{x}{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(-x + 1)} + 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1)ln(\frac{1}{x}) + (-x + 1)^{x}{\frac{1}{x}}^{x}ln^{4}(-x + 1) - 4{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(\frac{1}{x}) - \frac{19x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + \frac{(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{2}} - 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{3}(-x + 1) - \frac{8(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} + 3(-x + 1)^{x}{\frac{1}{x}}^{x}ln^{2}(-x + 1) + 6{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(\frac{1}{x}) + {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{4}(\frac{1}{x}) + \frac{26x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{19x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - {\frac{1}{x}}^{x}(-x + 1)^{x}ln^{3}(-x + 1) - 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln(-x + 1) + \frac{5(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)x} + \frac{11x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{4}} - \frac{6x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{4}} + \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)x} - 4{\frac{1}{x}}^{x}(-x + 1)^{x}ln(\frac{1}{x}) + \frac{x^{4}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{4}} + \frac{x^{3}{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{3}} + \frac{6x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{3}} + 3{\frac{1}{x}}^{x}(-x + 1)^{x}ln^{2}(-x + 1) - \frac{17x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} - \frac{5x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{3}} + \frac{3x^{2}{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)^{2}} + \frac{3x^{3}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{3}} - \frac{3(-x + 1)^{x}{\frac{1}{x}}^{x}}{x} - \frac{6x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{4}} + \frac{3x{\frac{1}{x}}^{x}(-x + 1)^{x}}{(-x + 1)} + \frac{3x^{2}(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)^{2}} - \frac{2(-x + 1)^{x}{\frac{1}{x}}^{x}}{x^{3}} - \frac{3{\frac{1}{x}}^{x}(-x + 1)^{x}}{x} - \frac{2{\frac{1}{x}}^{x}(-x + 1)^{x}}{x^{2}} - (-x + 1)^{x}{\frac{1}{x}}^{x}ln(-x + 1) + {\frac{1}{x}}^{x}(-x + 1)^{x} + \frac{x(-x + 1)^{x}{\frac{1}{x}}^{x}}{(-x + 1)}\\ \end{split}\end{equation} \]

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