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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{x}^{sin(arctan(x))} 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{x}^{sin(arctan(x))}\right)}{dx}\\=&(\frac{(\frac{(cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})}))}{(sin(arctan(x)))} - \frac{(1)log_{x}^{sin(arctan(x))}}{(x)})}{(ln(x))})\\=&\frac{cos(arctan(x))}{(x^{2} + 1)ln(x)sin(arctan(x))} - \frac{log_{x}^{sin(arctan(x))}}{xln(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cos(arctan(x))}{(x^{2} + 1)ln(x)sin(arctan(x))} - \frac{log_{x}^{sin(arctan(x))}}{xln(x)}\right)}{dx}\\=&\frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})cos(arctan(x))}{ln(x)sin(arctan(x))} + \frac{-cos(arctan(x))}{(x^{2} + 1)ln^{2}(x)(x)sin(arctan(x))} + \frac{-cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})})cos(arctan(x))}{(x^{2} + 1)ln(x)sin^{2}(arctan(x))} + \frac{-sin(arctan(x))(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)ln(x)sin(arctan(x))} - \frac{-log_{x}^{sin(arctan(x))}}{x^{2}ln(x)} - \frac{(\frac{(\frac{(cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})}))}{(sin(arctan(x)))} - \frac{(1)log_{x}^{sin(arctan(x))}}{(x)})}{(ln(x))})}{xln(x)} - \frac{log_{x}^{sin(arctan(x))}*-1}{xln^{2}(x)(x)}\\=&\frac{-2xcos(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin(arctan(x))} - \frac{2cos(arctan(x))}{(x^{2} + 1)xln^{2}(x)sin(arctan(x))} - \frac{cos^{2}(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin^{2}(arctan(x))} - \frac{1}{(x^{2} + 1)^{2}ln(x)} + \frac{log_{x}^{sin(arctan(x))}}{x^{2}ln(x)} + \frac{2log_{x}^{sin(arctan(x))}}{x^{2}ln^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2xcos(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin(arctan(x))} - \frac{2cos(arctan(x))}{(x^{2} + 1)xln^{2}(x)sin(arctan(x))} - \frac{cos^{2}(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin^{2}(arctan(x))} - \frac{1}{(x^{2} + 1)^{2}ln(x)} + \frac{log_{x}^{sin(arctan(x))}}{x^{2}ln(x)} + \frac{2log_{x}^{sin(arctan(x))}}{x^{2}ln^{2}(x)}\right)}{dx}\\=&\frac{-2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xcos(arctan(x))}{ln(x)sin(arctan(x))} - \frac{2cos(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin(arctan(x))} - \frac{2x*-cos(arctan(x))}{(x^{2} + 1)^{2}ln^{2}(x)(x)sin(arctan(x))} - \frac{2x*-cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})})cos(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin^{2}(arctan(x))} - \frac{2x*-sin(arctan(x))(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)^{2}ln(x)sin(arctan(x))} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})cos(arctan(x))}{xln^{2}(x)sin(arctan(x))} - \frac{2*-cos(arctan(x))}{(x^{2} + 1)x^{2}ln^{2}(x)sin(arctan(x))} - \frac{2*-2cos(arctan(x))}{(x^{2} + 1)xln^{3}(x)(x)sin(arctan(x))} - \frac{2*-cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})})cos(arctan(x))}{(x^{2} + 1)xln^{2}(x)sin^{2}(arctan(x))} - \frac{2*-sin(arctan(x))(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)xln^{2}(x)sin(arctan(x))} - \frac{(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})cos^{2}(arctan(x))}{ln(x)sin^{2}(arctan(x))} - \frac{-cos^{2}(arctan(x))}{(x^{2} + 1)^{2}ln^{2}(x)(x)sin^{2}(arctan(x))} - \frac{-2cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})})cos^{2}(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin^{3}(arctan(x))} - \frac{-2cos(arctan(x))sin(arctan(x))(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)^{2}ln(x)sin^{2}(arctan(x))} - \frac{(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})}{ln(x)} - \frac{-1}{(x^{2} + 1)^{2}ln^{2}(x)(x)} + \frac{-2log_{x}^{sin(arctan(x))}}{x^{3}ln(x)} + \frac{(\frac{(\frac{(cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})}))}{(sin(arctan(x)))} - \frac{(1)log_{x}^{sin(arctan(x))}}{(x)})}{(ln(x))})}{x^{2}ln(x)} + \frac{log_{x}^{sin(arctan(x))}*-1}{x^{2}ln^{2}(x)(x)} + \frac{2*-2log_{x}^{sin(arctan(x))}}{x^{3}ln^{2}(x)} + \frac{2(\frac{(\frac{(cos(arctan(x))(\frac{(1)}{(1 + (x)^{2})}))}{(sin(arctan(x)))} - \frac{(1)log_{x}^{sin(arctan(x))}}{(x)})}{(ln(x))})}{x^{2}ln^{2}(x)} + \frac{2log_{x}^{sin(arctan(x))}*-2}{x^{2}ln^{3}(x)(x)}\\=&\frac{8x^{2}cos(arctan(x))}{(x^{2} + 1)^{3}ln(x)sin(arctan(x))} - \frac{2cos(arctan(x))}{(x^{2} + 1)^{2}ln(x)sin(arctan(x))} + \frac{6cos(arctan(x))}{(x^{2} + 1)^{2}ln^{2}(x)sin(arctan(x))} + \frac{6xcos^{2}(arctan(x))}{(x^{2} + 1)^{3}ln(x)sin^{2}(arctan(x))} + \frac{3cos(arctan(x))}{(x^{2} + 1)x^{2}ln^{2}(x)sin(arctan(x))} + \frac{6cos(arctan(x))}{(x^{2} + 1)x^{2}ln^{3}(x)sin(arctan(x))} + \frac{3cos^{2}(arctan(x))}{(x^{2} + 1)^{2}xln^{2}(x)sin^{2}(arctan(x))} + \frac{6x}{(x^{2} + 1)^{3}ln(x)} + \frac{3}{(x^{2} + 1)^{2}xln^{2}(x)} + \frac{2cos^{3}(arctan(x))}{(x^{2} + 1)^{3}ln(x)sin^{3}(arctan(x))} + \frac{2cos(arctan(x))}{(x^{2} + 1)^{3}ln(x)sin(arctan(x))} - \frac{2log_{x}^{sin(arctan(x))}}{x^{3}ln(x)} - \frac{6log_{x}^{sin(arctan(x))}}{x^{3}ln^{2}(x)} - \frac{6log_{x}^{sin(arctan(x))}}{x^{3}ln^{3}(x)}\\ \end{split}\end{equation} \]
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