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 2 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数tan(x)cot(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(x)cot(x)\right)}{dx}\\=&sec^{2}(x)(1)cot(x) + tan(x)*-csc^{2}(x)\\=&cot(x)sec^{2}(x) - tan(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cot(x)sec^{2}(x) - tan(x)csc^{2}(x)\right)}{dx}\\=&-csc^{2}(x)sec^{2}(x) + cot(x)*2sec^{2}(x)tan(x) - sec^{2}(x)(1)csc^{2}(x) - tan(x)*-2csc^{2}(x)cot(x)\\=&-2sec^{2}(x)csc^{2}(x) + 2tan(x)cot(x)sec^{2}(x) + 2tan(x)cot(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sec^{2}(x)csc^{2}(x) + 2tan(x)cot(x)sec^{2}(x) + 2tan(x)cot(x)csc^{2}(x)\right)}{dx}\\=&-2*2sec^{2}(x)tan(x)csc^{2}(x) - 2sec^{2}(x)*-2csc^{2}(x)cot(x) + 2sec^{2}(x)(1)cot(x)sec^{2}(x) + 2tan(x)*-csc^{2}(x)sec^{2}(x) + 2tan(x)cot(x)*2sec^{2}(x)tan(x) + 2sec^{2}(x)(1)cot(x)csc^{2}(x) + 2tan(x)*-csc^{2}(x)csc^{2}(x) + 2tan(x)cot(x)*-2csc^{2}(x)cot(x)\\=&-6tan(x)sec^{2}(x)csc^{2}(x) + 6cot(x)sec^{2}(x)csc^{2}(x) + 2cot(x)sec^{4}(x) + 4tan^{2}(x)cot(x)sec^{2}(x) - 2tan(x)csc^{4}(x) - 4tan(x)cot^{2}(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -6tan(x)sec^{2}(x)csc^{2}(x) + 6cot(x)sec^{2}(x)csc^{2}(x) + 2cot(x)sec^{4}(x) + 4tan^{2}(x)cot(x)sec^{2}(x) - 2tan(x)csc^{4}(x) - 4tan(x)cot^{2}(x)csc^{2}(x)\right)}{dx}\\=&-6sec^{2}(x)(1)sec^{2}(x)csc^{2}(x) - 6tan(x)*2sec^{2}(x)tan(x)csc^{2}(x) - 6tan(x)sec^{2}(x)*-2csc^{2}(x)cot(x) + 6*-csc^{2}(x)sec^{2}(x)csc^{2}(x) + 6cot(x)*2sec^{2}(x)tan(x)csc^{2}(x) + 6cot(x)sec^{2}(x)*-2csc^{2}(x)cot(x) + 2*-csc^{2}(x)sec^{4}(x) + 2cot(x)*4sec^{4}(x)tan(x) + 4*2tan(x)sec^{2}(x)(1)cot(x)sec^{2}(x) + 4tan^{2}(x)*-csc^{2}(x)sec^{2}(x) + 4tan^{2}(x)cot(x)*2sec^{2}(x)tan(x) - 2sec^{2}(x)(1)csc^{4}(x) - 2tan(x)*-4csc^{4}(x)cot(x) - 4sec^{2}(x)(1)cot^{2}(x)csc^{2}(x) - 4tan(x)*-2cot(x)csc^{2}(x)csc^{2}(x) - 4tan(x)cot^{2}(x)*-2csc^{2}(x)cot(x)\\=&-8sec^{4}(x)csc^{2}(x) - 16tan^{2}(x)sec^{2}(x)csc^{2}(x) + 24tan(x)cot(x)sec^{2}(x)csc^{2}(x) - 8sec^{2}(x)csc^{4}(x) - 16cot^{2}(x)sec^{2}(x)csc^{2}(x) + 16tan(x)cot(x)sec^{4}(x) + 8tan^{3}(x)cot(x)sec^{2}(x) + 16tan(x)cot(x)csc^{4}(x) + 8tan(x)cot^{3}(x)csc^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数tan(cot(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(cot(x))\right)}{dx}\\=&sec^{2}(cot(x))(-csc^{2}(x))\\=&-sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&-2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) - sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&2tan(cot(x))sec^{2}(cot(x))csc^{4}(x) + 2cot(x)sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2tan(cot(x))sec^{2}(cot(x))csc^{4}(x) + 2cot(x)sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&2sec^{2}(cot(x))(-csc^{2}(x))sec^{2}(cot(x))csc^{4}(x) + 2tan(cot(x))*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) + 2tan(cot(x))sec^{2}(cot(x))*-4csc^{4}(x)cot(x) + 2*-csc^{2}(x)sec^{2}(cot(x))csc^{2}(x) + 2cot(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) + 2cot(x)sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&-2sec^{4}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))csc^{6}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 2sec^{2}(cot(x))csc^{4}(x) - 4cot^{2}(x)sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -2sec^{4}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))csc^{6}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 2sec^{2}(cot(x))csc^{4}(x) - 4cot^{2}(x)sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&-2*4sec^{4}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{6}(x) - 2sec^{4}(cot(x))*-6csc^{6}(x)cot(x) - 4*2tan(cot(x))sec^{2}(cot(x))(-csc^{2}(x))sec^{2}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))*-6csc^{6}(x)cot(x) - 12sec^{2}(cot(x))(-csc^{2}(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 12tan(cot(x))*-csc^{2}(x)sec^{2}(cot(x))csc^{4}(x) - 12tan(cot(x))cot(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))*-4csc^{4}(x)cot(x) - 2*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) - 2sec^{2}(cot(x))*-4csc^{4}(x)cot(x) - 4*-2cot(x)csc^{2}(x)sec^{2}(cot(x))csc^{2}(x) - 4cot^{2}(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) - 4cot^{2}(x)sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&16tan(cot(x))sec^{4}(cot(x))csc^{8}(x) + 16cot(x)sec^{2}(cot(x))csc^{4}(x) + 8tan^{3}(cot(x))sec^{2}(cot(x))csc^{8}(x) + 48tan^{2}(cot(x))cot(x)sec^{2}(cot(x))csc^{6}(x) + 24cot(x)sec^{4}(cot(x))csc^{6}(x) + 16tan(cot(x))sec^{2}(cot(x))csc^{6}(x) + 56tan(cot(x))cot^{2}(x)sec^{2}(cot(x))csc^{4}(x) + 8cot^{3}(x)sec^{2}(cot(x))csc^{2}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数tan(x)cot(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(x)cot(x)\right)}{dx}\\=&sec^{2}(x)(1)cot(x) + tan(x)*-csc^{2}(x)\\=&cot(x)sec^{2}(x) - tan(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cot(x)sec^{2}(x) - tan(x)csc^{2}(x)\right)}{dx}\\=&-csc^{2}(x)sec^{2}(x) + cot(x)*2sec^{2}(x)tan(x) - sec^{2}(x)(1)csc^{2}(x) - tan(x)*-2csc^{2}(x)cot(x)\\=&-2sec^{2}(x)csc^{2}(x) + 2tan(x)cot(x)sec^{2}(x) + 2tan(x)cot(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sec^{2}(x)csc^{2}(x) + 2tan(x)cot(x)sec^{2}(x) + 2tan(x)cot(x)csc^{2}(x)\right)}{dx}\\=&-2*2sec^{2}(x)tan(x)csc^{2}(x) - 2sec^{2}(x)*-2csc^{2}(x)cot(x) + 2sec^{2}(x)(1)cot(x)sec^{2}(x) + 2tan(x)*-csc^{2}(x)sec^{2}(x) + 2tan(x)cot(x)*2sec^{2}(x)tan(x) + 2sec^{2}(x)(1)cot(x)csc^{2}(x) + 2tan(x)*-csc^{2}(x)csc^{2}(x) + 2tan(x)cot(x)*-2csc^{2}(x)cot(x)\\=&-6tan(x)sec^{2}(x)csc^{2}(x) + 6cot(x)sec^{2}(x)csc^{2}(x) + 2cot(x)sec^{4}(x) + 4tan^{2}(x)cot(x)sec^{2}(x) - 2tan(x)csc^{4}(x) - 4tan(x)cot^{2}(x)csc^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -6tan(x)sec^{2}(x)csc^{2}(x) + 6cot(x)sec^{2}(x)csc^{2}(x) + 2cot(x)sec^{4}(x) + 4tan^{2}(x)cot(x)sec^{2}(x) - 2tan(x)csc^{4}(x) - 4tan(x)cot^{2}(x)csc^{2}(x)\right)}{dx}\\=&-6sec^{2}(x)(1)sec^{2}(x)csc^{2}(x) - 6tan(x)*2sec^{2}(x)tan(x)csc^{2}(x) - 6tan(x)sec^{2}(x)*-2csc^{2}(x)cot(x) + 6*-csc^{2}(x)sec^{2}(x)csc^{2}(x) + 6cot(x)*2sec^{2}(x)tan(x)csc^{2}(x) + 6cot(x)sec^{2}(x)*-2csc^{2}(x)cot(x) + 2*-csc^{2}(x)sec^{4}(x) + 2cot(x)*4sec^{4}(x)tan(x) + 4*2tan(x)sec^{2}(x)(1)cot(x)sec^{2}(x) + 4tan^{2}(x)*-csc^{2}(x)sec^{2}(x) + 4tan^{2}(x)cot(x)*2sec^{2}(x)tan(x) - 2sec^{2}(x)(1)csc^{4}(x) - 2tan(x)*-4csc^{4}(x)cot(x) - 4sec^{2}(x)(1)cot^{2}(x)csc^{2}(x) - 4tan(x)*-2cot(x)csc^{2}(x)csc^{2}(x) - 4tan(x)cot^{2}(x)*-2csc^{2}(x)cot(x)\\=&-8sec^{4}(x)csc^{2}(x) - 16tan^{2}(x)sec^{2}(x)csc^{2}(x) + 24tan(x)cot(x)sec^{2}(x)csc^{2}(x) - 8sec^{2}(x)csc^{4}(x) - 16cot^{2}(x)sec^{2}(x)csc^{2}(x) + 16tan(x)cot(x)sec^{4}(x) + 8tan^{3}(x)cot(x)sec^{2}(x) + 16tan(x)cot(x)csc^{4}(x) + 8tan(x)cot^{3}(x)csc^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数tan(cot(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(cot(x))\right)}{dx}\\=&sec^{2}(cot(x))(-csc^{2}(x))\\=&-sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&-2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) - sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&2tan(cot(x))sec^{2}(cot(x))csc^{4}(x) + 2cot(x)sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2tan(cot(x))sec^{2}(cot(x))csc^{4}(x) + 2cot(x)sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&2sec^{2}(cot(x))(-csc^{2}(x))sec^{2}(cot(x))csc^{4}(x) + 2tan(cot(x))*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) + 2tan(cot(x))sec^{2}(cot(x))*-4csc^{4}(x)cot(x) + 2*-csc^{2}(x)sec^{2}(cot(x))csc^{2}(x) + 2cot(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) + 2cot(x)sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&-2sec^{4}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))csc^{6}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 2sec^{2}(cot(x))csc^{4}(x) - 4cot^{2}(x)sec^{2}(cot(x))csc^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -2sec^{4}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))csc^{6}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 2sec^{2}(cot(x))csc^{4}(x) - 4cot^{2}(x)sec^{2}(cot(x))csc^{2}(x)\right)}{dx}\\=&-2*4sec^{4}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{6}(x) - 2sec^{4}(cot(x))*-6csc^{6}(x)cot(x) - 4*2tan(cot(x))sec^{2}(cot(x))(-csc^{2}(x))sec^{2}(cot(x))csc^{6}(x) - 4tan^{2}(cot(x))*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{6}(x) - 4tan^{2}(cot(x))sec^{2}(cot(x))*-6csc^{6}(x)cot(x) - 12sec^{2}(cot(x))(-csc^{2}(x))cot(x)sec^{2}(cot(x))csc^{4}(x) - 12tan(cot(x))*-csc^{2}(x)sec^{2}(cot(x))csc^{4}(x) - 12tan(cot(x))cot(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) - 12tan(cot(x))cot(x)sec^{2}(cot(x))*-4csc^{4}(x)cot(x) - 2*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{4}(x) - 2sec^{2}(cot(x))*-4csc^{4}(x)cot(x) - 4*-2cot(x)csc^{2}(x)sec^{2}(cot(x))csc^{2}(x) - 4cot^{2}(x)*2sec^{2}(cot(x))tan(cot(x))*-csc^{2}(x)csc^{2}(x) - 4cot^{2}(x)sec^{2}(cot(x))*-2csc^{2}(x)cot(x)\\=&16tan(cot(x))sec^{4}(cot(x))csc^{8}(x) + 16cot(x)sec^{2}(cot(x))csc^{4}(x) + 8tan^{3}(cot(x))sec^{2}(cot(x))csc^{8}(x) + 48tan^{2}(cot(x))cot(x)sec^{2}(cot(x))csc^{6}(x) + 24cot(x)sec^{4}(cot(x))csc^{6}(x) + 16tan(cot(x))sec^{2}(cot(x))csc^{6}(x) + 56tan(cot(x))cot^{2}(x)sec^{2}(cot(x))csc^{4}(x) + 8cot^{3}(x)sec^{2}(cot(x))csc^{2}(x)\\ \end{split}\end{equation} \]
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