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。
\[ \begin{equation}\begin{split}【1/1】求函数xtan(sin(cos(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( xtan(sin(cos(x)))\right)}{dx}\\=&tan(sin(cos(x))) + xsec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))\\=&tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\right)}{dx}\\=&sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x)) - sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-2cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 2sin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - x*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) - xcos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - xsin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-3*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3cos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 6*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin(x)cos(cos(x))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xcos(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)cos(cos(x))*-sin(x)cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xcos(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + x*3sin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin^{3}(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*3sin^{2}(x)cos(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)cos(cos(x))*-sin(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)*-sin(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))*3sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 2sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2x*3sin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)sec^{4}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))*4sec^{4}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 4sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4x*3sin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))*2tan(sin(cos(x)))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&4sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 12sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 8sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 8sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 16sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 16xsin^{4}(x)cos^{4}(cos(x))tan(sin(cos(x)))sec^{4}(sin(cos(x))) - 3xsin(cos(x))cos^{2}(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(cos(x))cos(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)sin(cos(x))sec^{2}(sin(cos(x))) + 6xsin(cos(x))sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6xcos^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 12xsin(cos(x))sin^{2}(x)cos(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{2}(x)cos^{3}(cos(x))cos(x)sec^{4}(sin(cos(x))) - 16xsin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{4}(x)sec^{2}(sin(cos(x))) - 8xsin^{4}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 18xsin^{2}(x)sin(cos(x))cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(cos(x))sin^{4}(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 16xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{2}(x)cos^{3}(cos(x))cos(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin^{4}(x)sin^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 8xsin^{4}(x)cos^{4}(cos(x))tan^{3}(sin(cos(x)))sec^{2}(sin(cos(x)))\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数xtan(sin(cos(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( xtan(sin(cos(x)))\right)}{dx}\\=&tan(sin(cos(x))) + xsec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))\\=&tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\right)}{dx}\\=&sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x)) - sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-2cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 2sin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - x*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) - xcos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - xsin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-3*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3cos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 6*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin(x)cos(cos(x))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xcos(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)cos(cos(x))*-sin(x)cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xcos(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + x*3sin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin^{3}(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*3sin^{2}(x)cos(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)cos(cos(x))*-sin(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)*-sin(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))*3sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 2sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2x*3sin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)sec^{4}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))*4sec^{4}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 4sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4x*3sin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))*2tan(sin(cos(x)))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&4sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 12sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 8sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 8sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 16sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 16xsin^{4}(x)cos^{4}(cos(x))tan(sin(cos(x)))sec^{4}(sin(cos(x))) - 3xsin(cos(x))cos^{2}(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(cos(x))cos(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)sin(cos(x))sec^{2}(sin(cos(x))) + 6xsin(cos(x))sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6xcos^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 12xsin(cos(x))sin^{2}(x)cos(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{2}(x)cos^{3}(cos(x))cos(x)sec^{4}(sin(cos(x))) - 16xsin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{4}(x)sec^{2}(sin(cos(x))) - 8xsin^{4}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 18xsin^{2}(x)sin(cos(x))cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(cos(x))sin^{4}(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 16xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{2}(x)cos^{3}(cos(x))cos(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin^{4}(x)sin^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 8xsin^{4}(x)cos^{4}(cos(x))tan^{3}(sin(cos(x)))sec^{2}(sin(cos(x)))\\ \end{split}\end{equation} \]
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