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。
\[ \begin{equation}\begin{split}【1/1】求函数{(1 + \frac{1}{x})}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{1}{x} + 1)^{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (\frac{1}{x} + 1)^{x}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))\\=&(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1) - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1) - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}}{x} - \frac{-(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x^{2}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)x}\\=&(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1) - \frac{2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1) - \frac{2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{2}}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{2}(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}*2ln(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{2(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x} - \frac{2*-(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x^{2}} - \frac{2((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{2(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)x(\frac{1}{x} + 1)} - \frac{(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{3}} - \frac{-3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{2}} + \frac{-2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{2}}\\=&(\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1) - \frac{3(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1) - \frac{3(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{3}}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{3}(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}*3ln^{2}(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{3(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{x} - \frac{3*-(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x^{2}} - \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}*2ln(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)x(\frac{1}{x} + 1)} - \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x^{3}} - \frac{3*-3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{4}} - \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} - \frac{3(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}x^{3}(\frac{1}{x} + 1)} + \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x^{2}} + \frac{3*-2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} + \frac{3(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}x^{2}(\frac{1}{x} + 1)} - \frac{2(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{5}} - \frac{2*-5(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{6}} - \frac{2((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{4}} + \frac{3*-4(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{5}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{4}} + \frac{3*-4(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{3}} - \frac{-3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{3}}\\=&(\frac{1}{x} + 1)^{x}ln^{4}(\frac{1}{x} + 1) - \frac{4(\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{6(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{6(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{8(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{12(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{12(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{4(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{3}} - \frac{12(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} - \frac{6(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{7}} + \frac{16(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{6}} + \frac{11(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{6}} - \frac{12(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{5}} - \frac{6(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{5}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{4}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(1 + \frac{1}{x})}^{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{1}{x} + 1)^{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (\frac{1}{x} + 1)^{x}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))\\=&(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1) - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1) - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}}{x} - \frac{-(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)x^{2}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)x}\\=&(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1) - \frac{2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1) - \frac{2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{2}}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{2}(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}*2ln(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{2(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x} - \frac{2*-(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x^{2}} - \frac{2((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{2(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)x(\frac{1}{x} + 1)} - \frac{(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{3}} - \frac{-3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{2}} + \frac{-2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{2}}\\=&(\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1) - \frac{3(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( (\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1) - \frac{3(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{2(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{3}}\right)}{dx}\\=&((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{3}(\frac{1}{x} + 1) + \frac{(\frac{1}{x} + 1)^{x}*3ln^{2}(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)} - \frac{3(\frac{-(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}})(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{x} - \frac{3*-(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x^{2}} - \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{3(\frac{1}{x} + 1)^{x}*2ln(\frac{1}{x} + 1)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)x(\frac{1}{x} + 1)} - \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x^{3}} - \frac{3*-3(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{4}} - \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} - \frac{3(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}x^{3}(\frac{1}{x} + 1)} + \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{x^{2}} + \frac{3*-2(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} + \frac{3(\frac{1}{x} + 1)^{x}(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{2}x^{2}(\frac{1}{x} + 1)} - \frac{2(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{5}} - \frac{2*-5(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{6}} - \frac{2((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3(\frac{-2(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{3}})(\frac{1}{x} + 1)^{x}}{x^{4}} + \frac{3*-4(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{5}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{3(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{4}} + \frac{3*-4(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{3((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{(\frac{-3(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)^{4}})(\frac{1}{x} + 1)^{x}}{x^{3}} - \frac{-3(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{((\frac{1}{x} + 1)^{x}((1)ln(\frac{1}{x} + 1) + \frac{(x)(\frac{-1}{x^{2}} + 0)}{(\frac{1}{x} + 1)}))}{(\frac{1}{x} + 1)^{3}x^{3}}\\=&(\frac{1}{x} + 1)^{x}ln^{4}(\frac{1}{x} + 1) - \frac{4(\frac{1}{x} + 1)^{x}ln^{3}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)x} - \frac{6(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{3}} + \frac{6(\frac{1}{x} + 1)^{x}ln^{2}(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{2}} - \frac{8(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{5}} + \frac{12(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{2}x^{4}} + \frac{12(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{4}} - \frac{4(\frac{1}{x} + 1)^{x}ln(\frac{1}{x} + 1)}{(\frac{1}{x} + 1)^{3}x^{3}} - \frac{12(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{5}} - \frac{6(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{7}} + \frac{16(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{3}x^{6}} + \frac{11(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{6}} - \frac{12(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{2}x^{5}} - \frac{6(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{5}} + \frac{(\frac{1}{x} + 1)^{x}}{(\frac{1}{x} + 1)^{4}x^{4}}\\ \end{split}\end{equation} \]
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