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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(tan(x)) - tan(sin(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(tan(x)) - tan(sin(x))\right)}{dx}\\=&cos(tan(x))sec^{2}(x)(1) - sec^{2}(sin(x))(cos(x))\\=&cos(tan(x))sec^{2}(x) - cos(x)sec^{2}(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(tan(x))sec^{2}(x) - cos(x)sec^{2}(sin(x))\right)}{dx}\\=&-sin(tan(x))sec^{2}(x)(1)sec^{2}(x) + cos(tan(x))*2sec^{2}(x)tan(x) - -sin(x)sec^{2}(sin(x)) - cos(x)*2sec^{2}(sin(x))tan(sin(x))cos(x)\\=&-sin(tan(x))sec^{4}(x) + 2cos(tan(x))tan(x)sec^{2}(x) + sin(x)sec^{2}(sin(x)) - 2cos^{2}(x)tan(sin(x))sec^{2}(sin(x))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(tan(x))sec^{4}(x) + 2cos(tan(x))tan(x)sec^{2}(x) + sin(x)sec^{2}(sin(x)) - 2cos^{2}(x)tan(sin(x))sec^{2}(sin(x))\right)}{dx}\\=&-cos(tan(x))sec^{2}(x)(1)sec^{4}(x) - sin(tan(x))*4sec^{4}(x)tan(x) + 2*-sin(tan(x))sec^{2}(x)(1)tan(x)sec^{2}(x) + 2cos(tan(x))sec^{2}(x)(1)sec^{2}(x) + 2cos(tan(x))tan(x)*2sec^{2}(x)tan(x) + cos(x)sec^{2}(sin(x)) + sin(x)*2sec^{2}(sin(x))tan(sin(x))cos(x) - 2*-2cos(x)sin(x)tan(sin(x))sec^{2}(sin(x)) - 2cos^{2}(x)sec^{2}(sin(x))(cos(x))sec^{2}(sin(x)) - 2cos^{2}(x)tan(sin(x))*2sec^{2}(sin(x))tan(sin(x))cos(x)\\=&-cos(tan(x))sec^{6}(x) - 6sin(tan(x))tan(x)sec^{4}(x) + 2cos(tan(x))sec^{4}(x) + 4cos(tan(x))tan^{2}(x)sec^{2}(x) + cos(x)sec^{2}(sin(x)) + 6sin(x)cos(x)tan(sin(x))sec^{2}(sin(x)) - 2cos^{3}(x)sec^{4}(sin(x)) - 4cos^{3}(x)tan^{2}(sin(x))sec^{2}(sin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos(tan(x))sec^{6}(x) - 6sin(tan(x))tan(x)sec^{4}(x) + 2cos(tan(x))sec^{4}(x) + 4cos(tan(x))tan^{2}(x)sec^{2}(x) + cos(x)sec^{2}(sin(x)) + 6sin(x)cos(x)tan(sin(x))sec^{2}(sin(x)) - 2cos^{3}(x)sec^{4}(sin(x)) - 4cos^{3}(x)tan^{2}(sin(x))sec^{2}(sin(x))\right)}{dx}\\=&--sin(tan(x))sec^{2}(x)(1)sec^{6}(x) - cos(tan(x))*6sec^{6}(x)tan(x) - 6cos(tan(x))sec^{2}(x)(1)tan(x)sec^{4}(x) - 6sin(tan(x))sec^{2}(x)(1)sec^{4}(x) - 6sin(tan(x))tan(x)*4sec^{4}(x)tan(x) + 2*-sin(tan(x))sec^{2}(x)(1)sec^{4}(x) + 2cos(tan(x))*4sec^{4}(x)tan(x) + 4*-sin(tan(x))sec^{2}(x)(1)tan^{2}(x)sec^{2}(x) + 4cos(tan(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4cos(tan(x))tan^{2}(x)*2sec^{2}(x)tan(x) + -sin(x)sec^{2}(sin(x)) + cos(x)*2sec^{2}(sin(x))tan(sin(x))cos(x) + 6cos(x)cos(x)tan(sin(x))sec^{2}(sin(x)) + 6sin(x)*-sin(x)tan(sin(x))sec^{2}(sin(x)) + 6sin(x)cos(x)sec^{2}(sin(x))(cos(x))sec^{2}(sin(x)) + 6sin(x)cos(x)tan(sin(x))*2sec^{2}(sin(x))tan(sin(x))cos(x) - 2*-3cos^{2}(x)sin(x)sec^{4}(sin(x)) - 2cos^{3}(x)*4sec^{4}(sin(x))tan(sin(x))cos(x) - 4*-3cos^{2}(x)sin(x)tan^{2}(sin(x))sec^{2}(sin(x)) - 4cos^{3}(x)*2tan(sin(x))sec^{2}(sin(x))(cos(x))sec^{2}(sin(x)) - 4cos^{3}(x)tan^{2}(sin(x))*2sec^{2}(sin(x))tan(sin(x))cos(x)\\=&sin(tan(x))sec^{8}(x) - 12cos(tan(x))tan(x)sec^{6}(x) + 16cos(tan(x))tan(x)sec^{4}(x) - 8sin(tan(x))sec^{6}(x) - 28sin(tan(x))tan^{2}(x)sec^{4}(x) + 8cos(tan(x))tan^{3}(x)sec^{2}(x) - sin(x)sec^{2}(sin(x)) - 16cos^{4}(x)tan(sin(x))sec^{4}(sin(x)) + 8cos^{2}(x)tan(sin(x))sec^{2}(sin(x)) - 6sin^{2}(x)tan(sin(x))sec^{2}(sin(x)) + 12sin(x)cos^{2}(x)sec^{4}(sin(x)) + 24sin(x)cos^{2}(x)tan^{2}(sin(x))sec^{2}(sin(x)) - 8cos^{4}(x)tan^{3}(sin(x))sec^{2}(sin(x))\\ \end{split}\end{equation} \]
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