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