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。
\[ \begin{equation}\begin{split}【1/1】求函数12345sin(x)cos(x)tan(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 12345sin(x)cos(x)tan(x)\right)}{dx}\\=&12345cos(x)cos(x)tan(x) + 12345sin(x)*-sin(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)(1)\\=&12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\right)}{dx}\\=&12345*-2cos(x)sin(x)tan(x) + 12345cos^{2}(x)sec^{2}(x)(1) - 12345*2sin(x)cos(x)tan(x) - 12345sin^{2}(x)sec^{2}(x)(1) + 12345cos(x)cos(x)sec^{2}(x) + 12345sin(x)*-sin(x)sec^{2}(x) + 12345sin(x)cos(x)*2sec^{2}(x)tan(x)\\=&24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\right)}{dx}\\=&24690cos(x)cos(x)tan(x)sec^{2}(x) + 24690sin(x)*-sin(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) + 24690sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + 24690*-2cos(x)sin(x)sec^{2}(x) + 24690cos^{2}(x)*2sec^{2}(x)tan(x) - 49380cos(x)cos(x)tan(x) - 49380sin(x)*-sin(x)tan(x) - 49380sin(x)cos(x)sec^{2}(x)(1) - 24690*2sin(x)cos(x)sec^{2}(x) - 24690sin^{2}(x)*2sec^{2}(x)tan(x)\\=&74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\right)}{dx}\\=&74070*-2cos(x)sin(x)tan(x)sec^{2}(x) + 74070cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 74070cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 74070*2sin(x)cos(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 74070sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) + 24690cos(x)cos(x)sec^{4}(x) + 24690sin(x)*-sin(x)sec^{4}(x) + 24690sin(x)cos(x)*4sec^{4}(x)tan(x) + 49380cos(x)cos(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 49380sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) - 148140cos(x)cos(x)sec^{2}(x) - 148140sin(x)*-sin(x)sec^{2}(x) - 148140sin(x)cos(x)*2sec^{2}(x)tan(x) - 49380*-2cos(x)sin(x)tan(x) - 49380cos^{2}(x)sec^{2}(x)(1) + 49380*2sin(x)cos(x)tan(x) + 49380sin^{2}(x)sec^{2}(x)(1)\\=&197520sin(x)cos(x)tan(x)sec^{4}(x) + 98760cos^{2}(x)sec^{4}(x) + 197520cos^{2}(x)tan^{2}(x)sec^{2}(x) - 592560sin(x)cos(x)tan(x)sec^{2}(x) - 98760sin^{2}(x)sec^{4}(x) - 197520sin^{2}(x)tan^{2}(x)sec^{2}(x) + 98760sin(x)cos(x)tan^{3}(x)sec^{2}(x) - 197520cos^{2}(x)sec^{2}(x) + 197520sin^{2}(x)sec^{2}(x) + 197520sin(x)cos(x)tan(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数12345sin(x)cos(x)tan(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 12345sin(x)cos(x)tan(x)\right)}{dx}\\=&12345cos(x)cos(x)tan(x) + 12345sin(x)*-sin(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)(1)\\=&12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 12345cos^{2}(x)tan(x) - 12345sin^{2}(x)tan(x) + 12345sin(x)cos(x)sec^{2}(x)\right)}{dx}\\=&12345*-2cos(x)sin(x)tan(x) + 12345cos^{2}(x)sec^{2}(x)(1) - 12345*2sin(x)cos(x)tan(x) - 12345sin^{2}(x)sec^{2}(x)(1) + 12345cos(x)cos(x)sec^{2}(x) + 12345sin(x)*-sin(x)sec^{2}(x) + 12345sin(x)cos(x)*2sec^{2}(x)tan(x)\\=&24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 24690sin(x)cos(x)tan(x)sec^{2}(x) + 24690cos^{2}(x)sec^{2}(x) - 49380sin(x)cos(x)tan(x) - 24690sin^{2}(x)sec^{2}(x)\right)}{dx}\\=&24690cos(x)cos(x)tan(x)sec^{2}(x) + 24690sin(x)*-sin(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) + 24690sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + 24690*-2cos(x)sin(x)sec^{2}(x) + 24690cos^{2}(x)*2sec^{2}(x)tan(x) - 49380cos(x)cos(x)tan(x) - 49380sin(x)*-sin(x)tan(x) - 49380sin(x)cos(x)sec^{2}(x)(1) - 24690*2sin(x)cos(x)sec^{2}(x) - 24690sin^{2}(x)*2sec^{2}(x)tan(x)\\=&74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 74070cos^{2}(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)tan(x)sec^{2}(x) + 24690sin(x)cos(x)sec^{4}(x) + 49380sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140sin(x)cos(x)sec^{2}(x) - 49380cos^{2}(x)tan(x) + 49380sin^{2}(x)tan(x)\right)}{dx}\\=&74070*-2cos(x)sin(x)tan(x)sec^{2}(x) + 74070cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 74070cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 74070*2sin(x)cos(x)tan(x)sec^{2}(x) - 74070sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 74070sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) + 24690cos(x)cos(x)sec^{4}(x) + 24690sin(x)*-sin(x)sec^{4}(x) + 24690sin(x)cos(x)*4sec^{4}(x)tan(x) + 49380cos(x)cos(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) + 49380sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 49380sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) - 148140cos(x)cos(x)sec^{2}(x) - 148140sin(x)*-sin(x)sec^{2}(x) - 148140sin(x)cos(x)*2sec^{2}(x)tan(x) - 49380*-2cos(x)sin(x)tan(x) - 49380cos^{2}(x)sec^{2}(x)(1) + 49380*2sin(x)cos(x)tan(x) + 49380sin^{2}(x)sec^{2}(x)(1)\\=&197520sin(x)cos(x)tan(x)sec^{4}(x) + 98760cos^{2}(x)sec^{4}(x) + 197520cos^{2}(x)tan^{2}(x)sec^{2}(x) - 592560sin(x)cos(x)tan(x)sec^{2}(x) - 98760sin^{2}(x)sec^{4}(x) - 197520sin^{2}(x)tan^{2}(x)sec^{2}(x) + 98760sin(x)cos(x)tan^{3}(x)sec^{2}(x) - 197520cos^{2}(x)sec^{2}(x) + 197520sin^{2}(x)sec^{2}(x) + 197520sin(x)cos(x)tan(x)\\ \end{split}\end{equation} \]
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