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。
\[ \begin{equation}\begin{split}【1/1】求函数cos(sec(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(sec(x))\right)}{dx}\\=&-sin(sec(x))sec(x)tan(x)\\=&-sin(sec(x))tan(x)sec(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sin(sec(x))tan(x)sec(x)\right)}{dx}\\=&-cos(sec(x))sec(x)tan(x)tan(x)sec(x) - sin(sec(x))sec^{2}(x)(1)sec(x) - sin(sec(x))tan(x)sec(x)tan(x)\\=&-cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\right)}{dx}\\=&--sin(sec(x))sec(x)tan(x)tan^{2}(x)sec^{2}(x) - cos(sec(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) - cos(sec(x))tan^{2}(x)*2sec^{2}(x)tan(x) - cos(sec(x))sec(x)tan(x)sec^{3}(x) - sin(sec(x))*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{2}(x)sec(x) - sin(sec(x))*2tan(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{2}(x)sec(x)tan(x)\\=&sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\right)}{dx}\\=&cos(sec(x))sec(x)tan(x)tan^{3}(x)sec^{3}(x) + sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x) + sin(sec(x))tan^{3}(x)*3sec^{3}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan(x)sec^{4}(x) - 3cos(sec(x))sec^{2}(x)(1)sec^{4}(x) - 3cos(sec(x))tan(x)*4sec^{4}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan^{3}(x)sec^{2}(x) - 3cos(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 3cos(sec(x))tan^{3}(x)*2sec^{2}(x)tan(x) - 5cos(sec(x))sec(x)tan(x)tan(x)sec^{3}(x) - 5sin(sec(x))sec^{2}(x)(1)sec^{3}(x) - 5sin(sec(x))tan(x)*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{3}(x)sec(x) - sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{3}(x)sec(x)tan(x)\\=&cos(sec(x))tan^{4}(x)sec^{4}(x) + 6sin(sec(x))tan^{2}(x)sec^{5}(x) + 6sin(sec(x))tan^{4}(x)sec^{3}(x) - 3cos(sec(x))sec^{6}(x) - 26cos(sec(x))tan^{2}(x)sec^{4}(x) - 7cos(sec(x))tan^{4}(x)sec^{2}(x) - 5sin(sec(x))sec^{5}(x) - 18sin(sec(x))tan^{2}(x)sec^{3}(x) - sin(sec(x))tan^{4}(x)sec(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数cos(sec(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(sec(x))\right)}{dx}\\=&-sin(sec(x))sec(x)tan(x)\\=&-sin(sec(x))tan(x)sec(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sin(sec(x))tan(x)sec(x)\right)}{dx}\\=&-cos(sec(x))sec(x)tan(x)tan(x)sec(x) - sin(sec(x))sec^{2}(x)(1)sec(x) - sin(sec(x))tan(x)sec(x)tan(x)\\=&-cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\right)}{dx}\\=&--sin(sec(x))sec(x)tan(x)tan^{2}(x)sec^{2}(x) - cos(sec(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) - cos(sec(x))tan^{2}(x)*2sec^{2}(x)tan(x) - cos(sec(x))sec(x)tan(x)sec^{3}(x) - sin(sec(x))*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{2}(x)sec(x) - sin(sec(x))*2tan(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{2}(x)sec(x)tan(x)\\=&sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\right)}{dx}\\=&cos(sec(x))sec(x)tan(x)tan^{3}(x)sec^{3}(x) + sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x) + sin(sec(x))tan^{3}(x)*3sec^{3}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan(x)sec^{4}(x) - 3cos(sec(x))sec^{2}(x)(1)sec^{4}(x) - 3cos(sec(x))tan(x)*4sec^{4}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan^{3}(x)sec^{2}(x) - 3cos(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 3cos(sec(x))tan^{3}(x)*2sec^{2}(x)tan(x) - 5cos(sec(x))sec(x)tan(x)tan(x)sec^{3}(x) - 5sin(sec(x))sec^{2}(x)(1)sec^{3}(x) - 5sin(sec(x))tan(x)*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{3}(x)sec(x) - sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{3}(x)sec(x)tan(x)\\=&cos(sec(x))tan^{4}(x)sec^{4}(x) + 6sin(sec(x))tan^{2}(x)sec^{5}(x) + 6sin(sec(x))tan^{4}(x)sec^{3}(x) - 3cos(sec(x))sec^{6}(x) - 26cos(sec(x))tan^{2}(x)sec^{4}(x) - 7cos(sec(x))tan^{4}(x)sec^{2}(x) - 5sin(sec(x))sec^{5}(x) - 18sin(sec(x))tan^{2}(x)sec^{3}(x) - sin(sec(x))tan^{4}(x)sec(x)\\ \end{split}\end{equation} \]
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