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 3 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{{x}^{x}}^{2{x}^{(3{x}^{4}x)}} 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = log_{{x}^{x}}^{2{x}^{(3x^{5})}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{{x}^{x}}^{2{x}^{(3x^{5})}}\right)}{dx}\\=&(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})\\=&\frac{-log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln({x}^{x})} + \frac{15x^{4}ln(x)}{ln({x}^{x})} + \frac{3x^{4}}{ln({x}^{x})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln({x}^{x})} + \frac{15x^{4}ln(x)}{ln({x}^{x})} + \frac{3x^{4}}{ln({x}^{x})}\right)}{dx}\\=&\frac{-(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})ln(x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{(x)ln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})} - \frac{(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})} + \frac{15*4x^{3}ln(x)}{ln({x}^{x})} + \frac{15x^{4}}{(x)ln({x}^{x})} + \frac{15x^{4}ln(x)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})} + \frac{3*4x^{3}}{ln({x}^{x})} + \frac{3x^{4}*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})}\\=&\frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{2}(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{2}({x}^{x})} - \frac{30x^{4}ln^{2}(x)}{ln^{2}({x}^{x})} - \frac{18x^{4}ln(x)}{ln^{2}({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{xln({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln^{2}({x}^{x})} - \frac{18x^{4}ln(x)}{ln^{2}({x}^{x})} + \frac{60x^{3}ln(x)}{ln({x}^{x})} - \frac{6x^{4}}{ln^{2}({x}^{x})} + \frac{27x^{3}}{ln({x}^{x})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{2}(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{2}({x}^{x})} - \frac{30x^{4}ln^{2}(x)}{ln^{2}({x}^{x})} - \frac{18x^{4}ln(x)}{ln^{2}({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{xln({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln^{2}({x}^{x})} - \frac{18x^{4}ln(x)}{ln^{2}({x}^{x})} + \frac{60x^{3}ln(x)}{ln({x}^{x})} - \frac{6x^{4}}{ln^{2}({x}^{x})} + \frac{27x^{3}}{ln({x}^{x})}\right)}{dx}\\=&\frac{2(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})ln^{2}(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}*2ln(x)}{(x)ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{2}(x)*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} + \frac{2(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})ln(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{ln^{3}({x}^{x})({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln^{2}({x}^{x})(x)} - \frac{30*4x^{3}ln^{2}(x)}{ln^{2}({x}^{x})} - \frac{30x^{4}*2ln(x)}{(x)ln^{2}({x}^{x})} - \frac{30x^{4}ln^{2}(x)*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} - \frac{18*4x^{3}ln(x)}{ln^{2}({x}^{x})} - \frac{18x^{4}*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{ln^{3}({x}^{x})({x}^{x})} - \frac{18x^{4}}{ln^{2}({x}^{x})(x)} - \frac{-log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{x^{2}ln({x}^{x})} - \frac{(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})}{xln({x}^{x})} - \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{xln^{2}({x}^{x})({x}^{x})} + \frac{2(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})ln(x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{(x)ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} + \frac{2(\frac{(\frac{(2({x}^{(3x^{5})}((3*5x^{4})ln(x) + \frac{(3x^{5})(1)}{(x)})))}{(2{x}^{(3x^{5})})} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{({x}^{x})})}{(ln({x}^{x}))})}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{2{x}^{(3x^{5})}}*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} - \frac{18*4x^{3}ln(x)}{ln^{2}({x}^{x})} - \frac{18x^{4}}{(x)ln^{2}({x}^{x})} - \frac{18x^{4}ln(x)*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} + \frac{60*3x^{2}ln(x)}{ln({x}^{x})} + \frac{60x^{3}}{(x)ln({x}^{x})} + \frac{60x^{3}ln(x)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})} - \frac{6*4x^{3}}{ln^{2}({x}^{x})} - \frac{6x^{4}*-2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{3}({x}^{x})({x}^{x})} + \frac{27*3x^{2}}{ln({x}^{x})} + \frac{27x^{3}*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})}\\=&\frac{-6log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{3}(x)}{ln^{3}({x}^{x})} - \frac{12log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{2}(x)}{ln^{3}({x}^{x})} + \frac{90x^{4}ln^{3}(x)}{ln^{3}({x}^{x})} + \frac{132x^{4}ln^{2}(x)}{ln^{3}({x}^{x})} + \frac{6log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{xln^{2}({x}^{x})} - \frac{6log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln^{2}(x)}{ln^{3}({x}^{x})} - \frac{12log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{3}({x}^{x})} + \frac{66x^{4}ln^{2}(x)}{ln^{3}({x}^{x})} + \frac{84x^{4}ln(x)}{ln^{3}({x}^{x})} + \frac{6log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{xln^{2}({x}^{x})} - \frac{180x^{3}ln^{2}(x)}{ln^{2}({x}^{x})} - \frac{174x^{3}ln(x)}{ln^{2}({x}^{x})} - \frac{132x^{3}ln(x)}{ln^{2}({x}^{x})} + \frac{180x^{2}ln(x)}{ln({x}^{x})} + \frac{log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{x^{2}ln({x}^{x})} + \frac{42x^{4}ln(x)}{ln^{3}({x}^{x})} - \frac{6log_{{x}^{x}}^{2{x}^{(3x^{5})}}ln(x)}{ln^{3}({x}^{x})} - \frac{6log_{{x}^{x}}^{2{x}^{(3x^{5})}}}{ln^{3}({x}^{x})} + \frac{18x^{4}}{ln^{3}({x}^{x})} - \frac{90x^{3}}{ln^{2}({x}^{x})} + \frac{141x^{2}}{ln({x}^{x})}\\ \end{split}\end{equation} \]
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