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 6 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{sin(x)}^{tan(x)} 关于 x 的 6 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 6 阶导数：} \\=&\frac{-720cos^{5}(x)sec^{2}(x)}{ln^{6}(sin(x))sin^{5}(x)tan(x)} - \frac{1440cos^{5}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{5}(x)tan(x)} - \frac{1440cos^{3}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{3}(x)tan(x)} - \frac{360cos^{4}(x)sec^{4}(x)}{ln^{5}(sin(x))sin^{4}(x)tan^{2}(x)} + \frac{720cos^{4}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{4}(x)} - \frac{1260cos^{5}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{5}(x)tan(x)} - \frac{1800cos^{3}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{3}(x)tan(x)} - \frac{540cos^{4}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{4}(x)tan^{2}(x)} + \frac{1080cos^{4}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{4}(x)} - \frac{540cos(x)sec^{2}(x)}{ln^{4}(sin(x))sin(x)tan(x)} - \frac{540cos^{2}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{1080cos^{2}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{2}(x)} - \frac{240cos^{3}(x)sec^{6}(x)}{ln^{4}(sin(x))sin^{3}(x)tan^{3}(x)} + \frac{480cos^{3}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{3}(x)tan(x)} - \frac{330cos^{4}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{4}(x)tan^{2}(x)} - \frac{600cos^{5}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{5}(x)tan(x)} - \frac{960cos^{3}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{3}(x)tan(x)} - \frac{420cos^{2}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{660cos^{4}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{4}(x)} - \frac{360cos(x)sec^{2}(x)}{ln^{3}(sin(x))sin(x)tan(x)} - \frac{240cos^{3}(x)sec^{6}(x)}{ln^{3}(sin(x))sin^{3}(x)tan^{3}(x)} + \frac{840cos^{2}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} - \frac{240cos(x)sec^{6}(x)}{ln^{3}(sin(x))sin(x)tan^{3}(x)} + \frac{480cos^{3}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{3}(x)tan(x)} - \frac{180cos^{2}(x)sec^{8}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{4}(x)} - \frac{90sec^{4}(x)}{ln^{3}(sin(x))tan^{2}(x)} + \frac{180sec^{2}(x)}{ln^{3}(sin(x))} + \frac{480cos^{2}(x)sec^{6}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{480cos(x)sec^{4}(x)}{ln^{3}(sin(x))sin(x)tan(x)} - \frac{80cos^{3}(x)sec^{6}(x)}{ln^{2}(sin(x))sin^{3}(x)tan^{3}(x)} - \frac{90cos^{4}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{4}(x)tan^{2}(x)} - \frac{120cos^{2}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{2}(x)} - \frac{360cos^{2}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{2}(x)} - \frac{80cos(x)sec^{6}(x)}{ln^{2}(sin(x))sin(x)tan^{3}(x)} + \frac{160cos^{3}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{3}(x)tan(x)} - \frac{144cos^{5}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{5}(x)tan(x)} - \frac{240cos^{3}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{3}(x)tan(x)} - \frac{90cos^{2}(x)sec^{8}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{4}(x)} + \frac{180cos^{4}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{4}(x)} - \frac{96cos(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)tan(x)} - \frac{144cos(x)sec^{10}(x)}{ln^{2}(sin(x))sin(x)tan^{5}(x)} + \frac{240cos^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} - \frac{30sec^{4}(x)}{ln^{2}(sin(x))tan^{2}(x)} + \frac{240cos^{2}(x)sec^{6}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{160cos(x)sec^{4}(x)}{ln^{2}(sin(x))sin(x)tan(x)} + \frac{480cos(x)sec^{8}(x)}{ln^{2}(sin(x))sin(x)tan^{3}(x)} + \frac{60sec^{2}(x)}{ln^{2}(sin(x))} + \frac{192cos(x)tan(x)sec^{4}(x)}{ln^{2}(sin(x))sin(x)} - \frac{160cos(x)tan(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)} - \frac{90sec^{8}(x)}{ln^{2}(sin(x))tan^{4}(x)} - \frac{480cos^{3}(x)tan(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{3}(x)} - \frac{480cos(x)tan(x)sec^{2}(x)}{ln^{3}(sin(x))sin(x)} - \frac{180cos^{2}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{240sec^{6}(x)}{ln^{2}(sin(x))tan^{2}(x)} - \frac{160cos^{3}(x)tan(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{3}(x)} - \frac{576cos(x)sec^{6}(x)}{ln^{2}(sin(x))sin(x)tan(x)} - \frac{180sec^{4}(x)}{ln^{2}(sin(x))} - \frac{120sec^{12}(x)}{ln(sin(x))tan^{6}(x)} + \frac{480sec^{10}(x)}{ln(sin(x))tan^{4}(x)} - \frac{480cos^{3}(x)tan(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{3}(x)} + \frac{240cos^{2}(x)tan^{2}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} + \frac{120cos^{2}(x)tan^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{120tan^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))} - \frac{96cos(x)tan^{3}(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)} - \frac{736sec^{8}(x)}{ln(sin(x))tan^{2}(x)} + \frac{544sec^{6}(x)}{ln(sin(x))} - \frac{80tan^{2}(x)sec^{4}(x)}{ln(sin(x))} + \frac{32tan^{4}(x)sec^{2}(x)}{ln(sin(x))} + \frac{720log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{6}(sin(x))sin^{6}(x)} + \frac{1800log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{5}(sin(x))sin^{6}(x)} + \frac{1800log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{5}(sin(x))sin^{4}(x)} + \frac{2040log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{4}(sin(x))sin^{6}(x)} + \frac{3120log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{4}(sin(x))sin^{4}(x)} + \frac{1080log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{4}(sin(x))sin^{2}(x)} + \frac{1350log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{3}(sin(x))sin^{6}(x)} + \frac{2430log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{3}(sin(x))sin^{4}(x)} + \frac{1170log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} + \frac{1060log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{2}(sin(x))sin^{4}(x)} + \frac{548log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{2}(sin(x))sin^{6}(x)} + \frac{572log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{136log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln(sin(x))sin^{2}(x)} + \frac{240log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln(sin(x))sin^{4}(x)} + \frac{120log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln(sin(x))sin^{6}(x)} + \frac{16log_{sin(x)}^{tan(x)}}{ln(sin(x))} + \frac{90log_{sin(x)}^{tan(x)}}{ln^{3}(sin(x))} + \frac{60log_{sin(x)}^{tan(x)}}{ln^{2}(sin(x))}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{sin(x)}^{tan(x)} 关于 x 的 6 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 6 阶导数：} \\=&\frac{-720cos^{5}(x)sec^{2}(x)}{ln^{6}(sin(x))sin^{5}(x)tan(x)} - \frac{1440cos^{5}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{5}(x)tan(x)} - \frac{1440cos^{3}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{3}(x)tan(x)} - \frac{360cos^{4}(x)sec^{4}(x)}{ln^{5}(sin(x))sin^{4}(x)tan^{2}(x)} + \frac{720cos^{4}(x)sec^{2}(x)}{ln^{5}(sin(x))sin^{4}(x)} - \frac{1260cos^{5}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{5}(x)tan(x)} - \frac{1800cos^{3}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{3}(x)tan(x)} - \frac{540cos^{4}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{4}(x)tan^{2}(x)} + \frac{1080cos^{4}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{4}(x)} - \frac{540cos(x)sec^{2}(x)}{ln^{4}(sin(x))sin(x)tan(x)} - \frac{540cos^{2}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{1080cos^{2}(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{2}(x)} - \frac{240cos^{3}(x)sec^{6}(x)}{ln^{4}(sin(x))sin^{3}(x)tan^{3}(x)} + \frac{480cos^{3}(x)sec^{4}(x)}{ln^{4}(sin(x))sin^{3}(x)tan(x)} - \frac{330cos^{4}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{4}(x)tan^{2}(x)} - \frac{600cos^{5}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{5}(x)tan(x)} - \frac{960cos^{3}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{3}(x)tan(x)} - \frac{420cos^{2}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{660cos^{4}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{4}(x)} - \frac{360cos(x)sec^{2}(x)}{ln^{3}(sin(x))sin(x)tan(x)} - \frac{240cos^{3}(x)sec^{6}(x)}{ln^{3}(sin(x))sin^{3}(x)tan^{3}(x)} + \frac{840cos^{2}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} - \frac{240cos(x)sec^{6}(x)}{ln^{3}(sin(x))sin(x)tan^{3}(x)} + \frac{480cos^{3}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{3}(x)tan(x)} - \frac{180cos^{2}(x)sec^{8}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{4}(x)} - \frac{90sec^{4}(x)}{ln^{3}(sin(x))tan^{2}(x)} + \frac{180sec^{2}(x)}{ln^{3}(sin(x))} + \frac{480cos^{2}(x)sec^{6}(x)}{ln^{3}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{480cos(x)sec^{4}(x)}{ln^{3}(sin(x))sin(x)tan(x)} - \frac{80cos^{3}(x)sec^{6}(x)}{ln^{2}(sin(x))sin^{3}(x)tan^{3}(x)} - \frac{90cos^{4}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{4}(x)tan^{2}(x)} - \frac{120cos^{2}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{2}(x)} - \frac{360cos^{2}(x)sec^{4}(x)}{ln^{3}(sin(x))sin^{2}(x)} - \frac{80cos(x)sec^{6}(x)}{ln^{2}(sin(x))sin(x)tan^{3}(x)} + \frac{160cos^{3}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{3}(x)tan(x)} - \frac{144cos^{5}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{5}(x)tan(x)} - \frac{240cos^{3}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{3}(x)tan(x)} - \frac{90cos^{2}(x)sec^{8}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{4}(x)} + \frac{180cos^{4}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{4}(x)} - \frac{96cos(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)tan(x)} - \frac{144cos(x)sec^{10}(x)}{ln^{2}(sin(x))sin(x)tan^{5}(x)} + \frac{240cos^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} - \frac{30sec^{4}(x)}{ln^{2}(sin(x))tan^{2}(x)} + \frac{240cos^{2}(x)sec^{6}(x)}{ln^{2}(sin(x))sin^{2}(x)tan^{2}(x)} + \frac{160cos(x)sec^{4}(x)}{ln^{2}(sin(x))sin(x)tan(x)} + \frac{480cos(x)sec^{8}(x)}{ln^{2}(sin(x))sin(x)tan^{3}(x)} + \frac{60sec^{2}(x)}{ln^{2}(sin(x))} + \frac{192cos(x)tan(x)sec^{4}(x)}{ln^{2}(sin(x))sin(x)} - \frac{160cos(x)tan(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)} - \frac{90sec^{8}(x)}{ln^{2}(sin(x))tan^{4}(x)} - \frac{480cos^{3}(x)tan(x)sec^{2}(x)}{ln^{4}(sin(x))sin^{3}(x)} - \frac{480cos(x)tan(x)sec^{2}(x)}{ln^{3}(sin(x))sin(x)} - \frac{180cos^{2}(x)sec^{4}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{240sec^{6}(x)}{ln^{2}(sin(x))tan^{2}(x)} - \frac{160cos^{3}(x)tan(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{3}(x)} - \frac{576cos(x)sec^{6}(x)}{ln^{2}(sin(x))sin(x)tan(x)} - \frac{180sec^{4}(x)}{ln^{2}(sin(x))} - \frac{120sec^{12}(x)}{ln(sin(x))tan^{6}(x)} + \frac{480sec^{10}(x)}{ln(sin(x))tan^{4}(x)} - \frac{480cos^{3}(x)tan(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{3}(x)} + \frac{240cos^{2}(x)tan^{2}(x)sec^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} + \frac{120cos^{2}(x)tan^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{120tan^{2}(x)sec^{2}(x)}{ln^{2}(sin(x))} - \frac{96cos(x)tan^{3}(x)sec^{2}(x)}{ln^{2}(sin(x))sin(x)} - \frac{736sec^{8}(x)}{ln(sin(x))tan^{2}(x)} + \frac{544sec^{6}(x)}{ln(sin(x))} - \frac{80tan^{2}(x)sec^{4}(x)}{ln(sin(x))} + \frac{32tan^{4}(x)sec^{2}(x)}{ln(sin(x))} + \frac{720log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{6}(sin(x))sin^{6}(x)} + \frac{1800log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{5}(sin(x))sin^{6}(x)} + \frac{1800log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{5}(sin(x))sin^{4}(x)} + \frac{2040log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{4}(sin(x))sin^{6}(x)} + \frac{3120log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{4}(sin(x))sin^{4}(x)} + \frac{1080log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{4}(sin(x))sin^{2}(x)} + \frac{1350log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{3}(sin(x))sin^{6}(x)} + \frac{2430log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{3}(sin(x))sin^{4}(x)} + \frac{1170log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{3}(sin(x))sin^{2}(x)} + \frac{1060log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln^{2}(sin(x))sin^{4}(x)} + \frac{548log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln^{2}(sin(x))sin^{6}(x)} + \frac{572log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln^{2}(sin(x))sin^{2}(x)} + \frac{136log_{sin(x)}^{tan(x)}cos^{2}(x)}{ln(sin(x))sin^{2}(x)} + \frac{240log_{sin(x)}^{tan(x)}cos^{4}(x)}{ln(sin(x))sin^{4}(x)} + \frac{120log_{sin(x)}^{tan(x)}cos^{6}(x)}{ln(sin(x))sin^{6}(x)} + \frac{16log_{sin(x)}^{tan(x)}}{ln(sin(x))} + \frac{90log_{sin(x)}^{tan(x)}}{ln^{3}(sin(x))} + \frac{60log_{sin(x)}^{tan(x)}}{ln^{2}(sin(x))}\\ \end{split}\end{equation} \]
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