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 2 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{({2}^{x} + {53}^{x} + {49069}^{x})}{3})}^{(\frac{3}{x})} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}\right)}{dx}\\=&((\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}((\frac{3*-1}{x^{2}})ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x}) + \frac{(\frac{3}{x})(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}))\\=&\frac{-3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{2}} + \frac{{2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{2}} + \frac{{2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x}\right)}{dx}\\=&\frac{-3*-2(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{3}} - \frac{3((\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}((\frac{3*-1}{x^{2}})ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x}) + \frac{(\frac{3}{x})(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}))ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{2}} - \frac{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{x^{2}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})} + \frac{(\frac{-(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}}){2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{x} + \frac{-{2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} + \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{2}^{x}((\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}((\frac{3*-1}{x^{2}})ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x}) + \frac{(\frac{3}{x})(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}))ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}*0}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x(2)} + \frac{(\frac{-(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}}){53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{x} + \frac{-{53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} + \frac{({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)}))(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{53}^{x}((\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}((\frac{3*-1}{x^{2}})ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x}) + \frac{(\frac{3}{x})(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}))ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}*0}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x(53)} + \frac{(\frac{-(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}}){49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{x} + \frac{-{49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} + \frac{({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)}))(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{49069}^{x}((\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}((\frac{3*-1}{x^{2}})ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x}) + \frac{(\frac{3}{x})(\frac{1}{3}({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + \frac{1}{3}({53}^{x}((1)ln(53) + \frac{(x)(0)}{(53)})) + \frac{1}{3}({49069}^{x}((1)ln(49069) + \frac{(x)(0)}{(49069)})))}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}))ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} + \frac{{49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}*0}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x(49069)}\\=&\frac{6(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{3}} + \frac{9(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{x^{4}} - \frac{3 * {2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} - \frac{3 * {53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} - \frac{3 * {49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} - \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)ln(2)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)ln(2)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)ln(53)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)ln(53)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)ln(49069)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)ln(49069)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} - \frac{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}{2}^{x}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} + \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} + \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} - \frac{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}{53}^{x}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} + \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} + \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} - \frac{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}{49069}^{x}ln(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{3}} + \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} + \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} - \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(49069)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} + \frac{{49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} - \frac{2 * {53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} + \frac{{2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} - \frac{2 * {2}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} + \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} + \frac{{53}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(53)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x} - \frac{2 * {49069}^{x}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})x^{2}} - \frac{{53}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(53)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} + \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(2)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}} - \frac{{2}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(2)}{3(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x} + \frac{{49069}^{(2x)}(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{(\frac{3}{x})}ln^{2}(49069)}{(\frac{1}{3} * {2}^{x} + \frac{1}{3} * {53}^{x} + \frac{1}{3} * {49069}^{x})^{2}x^{2}}\\ \end{split}\end{equation} \]
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