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 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{tan(x)}^{2}}{({sec(x)}^{2} - 1)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{tan^{2}(x)}{(sec^{2}(x) - 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{tan^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{2}(x) + \frac{2tan(x)sec^{2}(x)(1)}{(sec^{2}(x) - 1)}\\=&\frac{-2tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2tan(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2tan(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&-2(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{3}(x)sec^{2}(x) - \frac{2*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{2tan^{3}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 2(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan(x)sec^{2}(x) + \frac{2sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{2tan(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{8tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{10tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{8tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{10tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&8(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{4}(x)sec^{4}(x) + \frac{8*4tan^{3}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{8tan^{4}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} - 10(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{2}(x)sec^{4}(x) - \frac{10*2tan(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{10tan^{2}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 4(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{4}(x)sec^{2}(x) - \frac{4*4tan^{3}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 2(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})sec^{4}(x) + \frac{2*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)} + 4(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{2}(x)sec^{2}(x) + \frac{4*2tan(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{-48tan^{5}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{72tan^{3}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24tan(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16tan(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-48tan^{5}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{72tan^{3}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24tan(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16tan(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&-48(\frac{-4(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{5}})tan^{5}(x)sec^{6}(x) - \frac{48*5tan^{4}(x)sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} - \frac{48tan^{5}(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{4}} + 72(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{3}(x)sec^{6}(x) + \frac{72*3tan^{2}(x)sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{72tan^{3}(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} + 48(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{5}(x)sec^{4}(x) + \frac{48*5tan^{4}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} - 24(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan(x)sec^{6}(x) - \frac{24sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{24tan(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 64(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{3}(x)sec^{4}(x) - \frac{64*3tan^{2}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 8(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{5}(x)sec^{2}(x) - \frac{8*5tan^{4}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 16(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan(x)sec^{4}(x) + \frac{16sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{16tan(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)} + 8(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{3}(x)sec^{2}(x) + \frac{8*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{384tan^{6}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{5}} - \frac{672tan^{4}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{4}} - \frac{576tan^{6}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{312tan^{2}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{928tan^{4}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{224tan^{6}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24sec^{8}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{368tan^{2}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{312tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{16tan^{6}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16sec^{6}(x)}{(sec^{2}(x) - 1)} + \frac{88tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{16tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{tan(x)}^{2}}{({sec(x)}^{2} - 1)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{tan^{2}(x)}{(sec^{2}(x) - 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{tan^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{2}(x) + \frac{2tan(x)sec^{2}(x)(1)}{(sec^{2}(x) - 1)}\\=&\frac{-2tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2tan(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2tan(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&-2(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{3}(x)sec^{2}(x) - \frac{2*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{2tan^{3}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 2(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan(x)sec^{2}(x) + \frac{2sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{2tan(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{8tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{10tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{8tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{10tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{2sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&8(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{4}(x)sec^{4}(x) + \frac{8*4tan^{3}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{8tan^{4}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} - 10(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{2}(x)sec^{4}(x) - \frac{10*2tan(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{10tan^{2}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 4(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{4}(x)sec^{2}(x) - \frac{4*4tan^{3}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{4tan^{4}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 2(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})sec^{4}(x) + \frac{2*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)} + 4(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{2}(x)sec^{2}(x) + \frac{4*2tan(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{4tan^{2}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{-48tan^{5}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{72tan^{3}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24tan(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16tan(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-48tan^{5}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{72tan^{3}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24tan(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16tan(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\right)}{dx}\\=&-48(\frac{-4(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{5}})tan^{5}(x)sec^{6}(x) - \frac{48*5tan^{4}(x)sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} - \frac{48tan^{5}(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{4}} + 72(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{3}(x)sec^{6}(x) + \frac{72*3tan^{2}(x)sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{72tan^{3}(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} + 48(\frac{-3(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{4}})tan^{5}(x)sec^{4}(x) + \frac{48*5tan^{4}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{48tan^{5}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{3}} - 24(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan(x)sec^{6}(x) - \frac{24sec^{2}(x)(1)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{24tan(x)*6sec^{6}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 64(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{3}(x)sec^{4}(x) - \frac{64*3tan^{2}(x)sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{64tan^{3}(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} - 8(\frac{-2(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{3}})tan^{5}(x)sec^{2}(x) - \frac{8*5tan^{4}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{8tan^{5}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)^{2}} + 16(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan(x)sec^{4}(x) + \frac{16sec^{2}(x)(1)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{16tan(x)*4sec^{4}(x)tan(x)}{(sec^{2}(x) - 1)} + 8(\frac{-(2sec^{2}(x)tan(x) + 0)}{(sec^{2}(x) - 1)^{2}})tan^{3}(x)sec^{2}(x) + \frac{8*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x)}{(sec^{2}(x) - 1)} + \frac{8tan^{3}(x)*2sec^{2}(x)tan(x)}{(sec^{2}(x) - 1)}\\=&\frac{384tan^{6}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{5}} - \frac{672tan^{4}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{4}} - \frac{576tan^{6}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{4}} + \frac{312tan^{2}(x)sec^{8}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{928tan^{4}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{3}} + \frac{224tan^{6}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{3}} - \frac{24sec^{8}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{368tan^{2}(x)sec^{6}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{312tan^{4}(x)sec^{4}(x)}{(sec^{2}(x) - 1)^{2}} - \frac{16tan^{6}(x)sec^{2}(x)}{(sec^{2}(x) - 1)^{2}} + \frac{16sec^{6}(x)}{(sec^{2}(x) - 1)} + \frac{88tan^{2}(x)sec^{4}(x)}{(sec^{2}(x) - 1)} + \frac{16tan^{4}(x)sec^{2}(x)}{(sec^{2}(x) - 1)}\\ \end{split}\end{equation} \]
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