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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(x)cos(x) - {sin(x)}^{2}tan(x) + sin(x)sec(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x)cos(x) - sin^{2}(x)tan(x) + sin(x)sec(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x)cos(x) - sin^{2}(x)tan(x) + sin(x)sec(x)\right)}{dx}\\=&cos(x)cos(x) + sin(x)*-sin(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x)(1) + cos(x)sec(x) + sin(x)sec(x)tan(x)\\=&cos(x)sec(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x) + sin(x)tan(x)sec(x) + cos^{2}(x) - sin^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(x)sec(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x) + sin(x)tan(x)sec(x) + cos^{2}(x) - sin^{2}(x)\right)}{dx}\\=&-sin(x)sec(x) + cos(x)sec(x)tan(x) - 2cos(x)cos(x)tan(x) - 2sin(x)*-sin(x)tan(x) - 2sin(x)cos(x)sec^{2}(x)(1) - 2sin(x)cos(x)sec^{2}(x) - sin^{2}(x)*2sec^{2}(x)tan(x) + cos(x)tan(x)sec(x) + sin(x)sec^{2}(x)(1)sec(x) + sin(x)tan(x)sec(x)tan(x) + -2cos(x)sin(x) - 2sin(x)cos(x)\\=& - sin(x)sec(x) + 2cos(x)tan(x)sec(x) - 2cos^{2}(x)tan(x) - 2sin^{2}(x)tan(x)sec^{2}(x) - 4sin(x)cos(x)sec^{2}(x) + sin(x)tan^{2}(x)sec(x) + sin(x)sec^{3}(x) + 2sin^{2}(x)tan(x) - 4sin(x)cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - sin(x)sec(x) + 2cos(x)tan(x)sec(x) - 2cos^{2}(x)tan(x) - 2sin^{2}(x)tan(x)sec^{2}(x) - 4sin(x)cos(x)sec^{2}(x) + sin(x)tan^{2}(x)sec(x) + sin(x)sec^{3}(x) + 2sin^{2}(x)tan(x) - 4sin(x)cos(x)\right)}{dx}\\=& - cos(x)sec(x) - sin(x)sec(x)tan(x) + 2*-sin(x)tan(x)sec(x) + 2cos(x)sec^{2}(x)(1)sec(x) + 2cos(x)tan(x)sec(x)tan(x) - 2*-2cos(x)sin(x)tan(x) - 2cos^{2}(x)sec^{2}(x)(1) - 2*2sin(x)cos(x)tan(x)sec^{2}(x) - 2sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 2sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 4cos(x)cos(x)sec^{2}(x) - 4sin(x)*-sin(x)sec^{2}(x) - 4sin(x)cos(x)*2sec^{2}(x)tan(x) + cos(x)tan^{2}(x)sec(x) + sin(x)*2tan(x)sec^{2}(x)(1)sec(x) + sin(x)tan^{2}(x)sec(x)tan(x) + cos(x)sec^{3}(x) + sin(x)*3sec^{3}(x)tan(x) + 2*2sin(x)cos(x)tan(x) + 2sin^{2}(x)sec^{2}(x)(1) - 4cos(x)cos(x) - 4sin(x)*-sin(x)\\=&3cos(x)sec^{3}(x) - 3sin(x)tan(x)sec(x) + 5sin(x)tan(x)sec^{3}(x) - cos(x)sec(x) + 3cos(x)tan^{2}(x)sec(x) - 12sin(x)cos(x)tan(x)sec^{2}(x) - 6cos^{2}(x)sec^{2}(x) - 2sin^{2}(x)sec^{4}(x) - 4sin^{2}(x)tan^{2}(x)sec^{2}(x) + 6sin^{2}(x)sec^{2}(x) + 8sin(x)cos(x)tan(x) + sin(x)tan^{3}(x)sec(x) - 4cos^{2}(x) + 4sin^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 3cos(x)sec^{3}(x) - 3sin(x)tan(x)sec(x) + 5sin(x)tan(x)sec^{3}(x) - cos(x)sec(x) + 3cos(x)tan^{2}(x)sec(x) - 12sin(x)cos(x)tan(x)sec^{2}(x) - 6cos^{2}(x)sec^{2}(x) - 2sin^{2}(x)sec^{4}(x) - 4sin^{2}(x)tan^{2}(x)sec^{2}(x) + 6sin^{2}(x)sec^{2}(x) + 8sin(x)cos(x)tan(x) + sin(x)tan^{3}(x)sec(x) - 4cos^{2}(x) + 4sin^{2}(x)\right)}{dx}\\=&3*-sin(x)sec^{3}(x) + 3cos(x)*3sec^{3}(x)tan(x) - 3cos(x)tan(x)sec(x) - 3sin(x)sec^{2}(x)(1)sec(x) - 3sin(x)tan(x)sec(x)tan(x) + 5cos(x)tan(x)sec^{3}(x) + 5sin(x)sec^{2}(x)(1)sec^{3}(x) + 5sin(x)tan(x)*3sec^{3}(x)tan(x) - -sin(x)sec(x) - cos(x)sec(x)tan(x) + 3*-sin(x)tan^{2}(x)sec(x) + 3cos(x)*2tan(x)sec^{2}(x)(1)sec(x) + 3cos(x)tan^{2}(x)sec(x)tan(x) - 12cos(x)cos(x)tan(x)sec^{2}(x) - 12sin(x)*-sin(x)tan(x)sec^{2}(x) - 12sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) - 12sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) - 6*-2cos(x)sin(x)sec^{2}(x) - 6cos^{2}(x)*2sec^{2}(x)tan(x) - 2*2sin(x)cos(x)sec^{4}(x) - 2sin^{2}(x)*4sec^{4}(x)tan(x) - 4*2sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 4sin^{2}(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 4sin^{2}(x)tan^{2}(x)*2sec^{2}(x)tan(x) + 6*2sin(x)cos(x)sec^{2}(x) + 6sin^{2}(x)*2sec^{2}(x)tan(x) + 8cos(x)cos(x)tan(x) + 8sin(x)*-sin(x)tan(x) + 8sin(x)cos(x)sec^{2}(x)(1) + cos(x)tan^{3}(x)sec(x) + sin(x)*3tan^{2}(x)sec^{2}(x)(1)sec(x) + sin(x)tan^{3}(x)sec(x)tan(x) - 4*-2cos(x)sin(x) + 4*2sin(x)cos(x)\\=& - 6sin(x)sec^{3}(x) + 20cos(x)tan(x)sec^{3}(x) - 4cos(x)tan(x)sec(x) - 6sin(x)tan^{2}(x)sec(x) + 5sin(x)sec^{5}(x) + 18sin(x)tan^{2}(x)sec^{3}(x) + sin(x)sec(x) - 16sin^{2}(x)tan(x)sec^{4}(x) + 4cos(x)tan^{3}(x)sec(x) - 24cos^{2}(x)tan(x)sec^{2}(x) + 24sin^{2}(x)tan(x)sec^{2}(x) - 16sin(x)cos(x)sec^{4}(x) - 32sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 32sin(x)cos(x)sec^{2}(x) - 8sin^{2}(x)tan^{3}(x)sec^{2}(x) + 8cos^{2}(x)tan(x) + sin(x)tan^{4}(x)sec(x) - 8sin^{2}(x)tan(x) + 16sin(x)cos(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(x)cos(x) - {sin(x)}^{2}tan(x) + sin(x)sec(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x)cos(x) - sin^{2}(x)tan(x) + sin(x)sec(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x)cos(x) - sin^{2}(x)tan(x) + sin(x)sec(x)\right)}{dx}\\=&cos(x)cos(x) + sin(x)*-sin(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x)(1) + cos(x)sec(x) + sin(x)sec(x)tan(x)\\=&cos(x)sec(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x) + sin(x)tan(x)sec(x) + cos^{2}(x) - sin^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(x)sec(x) - 2sin(x)cos(x)tan(x) - sin^{2}(x)sec^{2}(x) + sin(x)tan(x)sec(x) + cos^{2}(x) - sin^{2}(x)\right)}{dx}\\=&-sin(x)sec(x) + cos(x)sec(x)tan(x) - 2cos(x)cos(x)tan(x) - 2sin(x)*-sin(x)tan(x) - 2sin(x)cos(x)sec^{2}(x)(1) - 2sin(x)cos(x)sec^{2}(x) - sin^{2}(x)*2sec^{2}(x)tan(x) + cos(x)tan(x)sec(x) + sin(x)sec^{2}(x)(1)sec(x) + sin(x)tan(x)sec(x)tan(x) + -2cos(x)sin(x) - 2sin(x)cos(x)\\=& - sin(x)sec(x) + 2cos(x)tan(x)sec(x) - 2cos^{2}(x)tan(x) - 2sin^{2}(x)tan(x)sec^{2}(x) - 4sin(x)cos(x)sec^{2}(x) + sin(x)tan^{2}(x)sec(x) + sin(x)sec^{3}(x) + 2sin^{2}(x)tan(x) - 4sin(x)cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - sin(x)sec(x) + 2cos(x)tan(x)sec(x) - 2cos^{2}(x)tan(x) - 2sin^{2}(x)tan(x)sec^{2}(x) - 4sin(x)cos(x)sec^{2}(x) + sin(x)tan^{2}(x)sec(x) + sin(x)sec^{3}(x) + 2sin^{2}(x)tan(x) - 4sin(x)cos(x)\right)}{dx}\\=& - cos(x)sec(x) - sin(x)sec(x)tan(x) + 2*-sin(x)tan(x)sec(x) + 2cos(x)sec^{2}(x)(1)sec(x) + 2cos(x)tan(x)sec(x)tan(x) - 2*-2cos(x)sin(x)tan(x) - 2cos^{2}(x)sec^{2}(x)(1) - 2*2sin(x)cos(x)tan(x)sec^{2}(x) - 2sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 2sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 4cos(x)cos(x)sec^{2}(x) - 4sin(x)*-sin(x)sec^{2}(x) - 4sin(x)cos(x)*2sec^{2}(x)tan(x) + cos(x)tan^{2}(x)sec(x) + sin(x)*2tan(x)sec^{2}(x)(1)sec(x) + sin(x)tan^{2}(x)sec(x)tan(x) + cos(x)sec^{3}(x) + sin(x)*3sec^{3}(x)tan(x) + 2*2sin(x)cos(x)tan(x) + 2sin^{2}(x)sec^{2}(x)(1) - 4cos(x)cos(x) - 4sin(x)*-sin(x)\\=&3cos(x)sec^{3}(x) - 3sin(x)tan(x)sec(x) + 5sin(x)tan(x)sec^{3}(x) - cos(x)sec(x) + 3cos(x)tan^{2}(x)sec(x) - 12sin(x)cos(x)tan(x)sec^{2}(x) - 6cos^{2}(x)sec^{2}(x) - 2sin^{2}(x)sec^{4}(x) - 4sin^{2}(x)tan^{2}(x)sec^{2}(x) + 6sin^{2}(x)sec^{2}(x) + 8sin(x)cos(x)tan(x) + sin(x)tan^{3}(x)sec(x) - 4cos^{2}(x) + 4sin^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 3cos(x)sec^{3}(x) - 3sin(x)tan(x)sec(x) + 5sin(x)tan(x)sec^{3}(x) - cos(x)sec(x) + 3cos(x)tan^{2}(x)sec(x) - 12sin(x)cos(x)tan(x)sec^{2}(x) - 6cos^{2}(x)sec^{2}(x) - 2sin^{2}(x)sec^{4}(x) - 4sin^{2}(x)tan^{2}(x)sec^{2}(x) + 6sin^{2}(x)sec^{2}(x) + 8sin(x)cos(x)tan(x) + sin(x)tan^{3}(x)sec(x) - 4cos^{2}(x) + 4sin^{2}(x)\right)}{dx}\\=&3*-sin(x)sec^{3}(x) + 3cos(x)*3sec^{3}(x)tan(x) - 3cos(x)tan(x)sec(x) - 3sin(x)sec^{2}(x)(1)sec(x) - 3sin(x)tan(x)sec(x)tan(x) + 5cos(x)tan(x)sec^{3}(x) + 5sin(x)sec^{2}(x)(1)sec^{3}(x) + 5sin(x)tan(x)*3sec^{3}(x)tan(x) - -sin(x)sec(x) - cos(x)sec(x)tan(x) + 3*-sin(x)tan^{2}(x)sec(x) + 3cos(x)*2tan(x)sec^{2}(x)(1)sec(x) + 3cos(x)tan^{2}(x)sec(x)tan(x) - 12cos(x)cos(x)tan(x)sec^{2}(x) - 12sin(x)*-sin(x)tan(x)sec^{2}(x) - 12sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) - 12sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) - 6*-2cos(x)sin(x)sec^{2}(x) - 6cos^{2}(x)*2sec^{2}(x)tan(x) - 2*2sin(x)cos(x)sec^{4}(x) - 2sin^{2}(x)*4sec^{4}(x)tan(x) - 4*2sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 4sin^{2}(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 4sin^{2}(x)tan^{2}(x)*2sec^{2}(x)tan(x) + 6*2sin(x)cos(x)sec^{2}(x) + 6sin^{2}(x)*2sec^{2}(x)tan(x) + 8cos(x)cos(x)tan(x) + 8sin(x)*-sin(x)tan(x) + 8sin(x)cos(x)sec^{2}(x)(1) + cos(x)tan^{3}(x)sec(x) + sin(x)*3tan^{2}(x)sec^{2}(x)(1)sec(x) + sin(x)tan^{3}(x)sec(x)tan(x) - 4*-2cos(x)sin(x) + 4*2sin(x)cos(x)\\=& - 6sin(x)sec^{3}(x) + 20cos(x)tan(x)sec^{3}(x) - 4cos(x)tan(x)sec(x) - 6sin(x)tan^{2}(x)sec(x) + 5sin(x)sec^{5}(x) + 18sin(x)tan^{2}(x)sec^{3}(x) + sin(x)sec(x) - 16sin^{2}(x)tan(x)sec^{4}(x) + 4cos(x)tan^{3}(x)sec(x) - 24cos^{2}(x)tan(x)sec^{2}(x) + 24sin^{2}(x)tan(x)sec^{2}(x) - 16sin(x)cos(x)sec^{4}(x) - 32sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 32sin(x)cos(x)sec^{2}(x) - 8sin^{2}(x)tan^{3}(x)sec^{2}(x) + 8cos^{2}(x)tan(x) + sin(x)tan^{4}(x)sec(x) - 8sin^{2}(x)tan(x) + 16sin(x)cos(x)\\ \end{split}\end{equation} \]
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