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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(x)cos(x)sin(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x)sin(cos(x))cos(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x)sin(cos(x))cos(x)\right)}{dx}\\=&cos(x)sin(cos(x))cos(x) + sin(x)cos(cos(x))*-sin(x)cos(x) + sin(x)sin(cos(x))*-sin(x)\\=&-sin^{2}(x)cos(cos(x))cos(x) + sin(cos(x))cos^{2}(x) - sin^{2}(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sin^{2}(x)cos(cos(x))cos(x) + sin(cos(x))cos^{2}(x) - sin^{2}(x)sin(cos(x))\right)}{dx}\\=&-2sin(x)cos(x)cos(cos(x))cos(x) - sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x) - sin^{2}(x)cos(cos(x))*-sin(x) + cos(cos(x))*-sin(x)cos^{2}(x) + sin(cos(x))*-2cos(x)sin(x) - 2sin(x)cos(x)sin(cos(x)) - sin^{2}(x)cos(cos(x))*-sin(x)\\=&-2sin(x)cos^{2}(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)cos(x) - sin(x)cos(cos(x))cos^{2}(x) + 2sin^{3}(x)cos(cos(x)) - 4sin(x)sin(cos(x))cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sin(x)cos^{2}(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)cos(x) - sin(x)cos(cos(x))cos^{2}(x) + 2sin^{3}(x)cos(cos(x)) - 4sin(x)sin(cos(x))cos(x)\right)}{dx}\\=&-2cos(x)cos^{2}(x)cos(cos(x)) - 2sin(x)*-2cos(x)sin(x)cos(cos(x)) - 2sin(x)cos^{2}(x)*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin^{3}(x)cos(x) - sin(cos(x))*3sin^{2}(x)cos(x)cos(x) - sin(cos(x))sin^{3}(x)*-sin(x) - cos(x)cos(cos(x))cos^{2}(x) - sin(x)*-sin(cos(x))*-sin(x)cos^{2}(x) - sin(x)cos(cos(x))*-2cos(x)sin(x) + 2*3sin^{2}(x)cos(x)cos(cos(x)) + 2sin^{3}(x)*-sin(cos(x))*-sin(x) - 4cos(x)sin(cos(x))cos(x) - 4sin(x)cos(cos(x))*-sin(x)cos(x) - 4sin(x)sin(cos(x))*-sin(x)\\=&-3cos^{3}(x)cos(cos(x)) + 10sin^{2}(x)cos(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos^{2}(x) + sin^{4}(x)cos(cos(x))cos(x) - 3sin^{2}(x)sin(cos(x))cos^{2}(x) + 3sin(cos(x))sin^{4}(x) + 6sin^{2}(x)cos(cos(x))cos(x) - 4sin(cos(x))cos^{2}(x) + 4sin^{2}(x)sin(cos(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -3cos^{3}(x)cos(cos(x)) + 10sin^{2}(x)cos(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos^{2}(x) + sin^{4}(x)cos(cos(x))cos(x) - 3sin^{2}(x)sin(cos(x))cos^{2}(x) + 3sin(cos(x))sin^{4}(x) + 6sin^{2}(x)cos(cos(x))cos(x) - 4sin(cos(x))cos^{2}(x) + 4sin^{2}(x)sin(cos(x))\right)}{dx}\\=&-3*-3cos^{2}(x)sin(x)cos(cos(x)) - 3cos^{3}(x)*-sin(cos(x))*-sin(x) + 10*2sin(x)cos(x)cos(x)cos(cos(x)) + 10sin^{2}(x)*-sin(x)cos(cos(x)) + 10sin^{2}(x)cos(x)*-sin(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)cos^{2}(x) - 3sin(cos(x))*2sin(x)cos(x)cos^{2}(x) - 3sin(cos(x))sin^{2}(x)*-2cos(x)sin(x) + 4sin^{3}(x)cos(x)cos(cos(x))cos(x) + sin^{4}(x)*-sin(cos(x))*-sin(x)cos(x) + sin^{4}(x)cos(cos(x))*-sin(x) - 3*2sin(x)cos(x)sin(cos(x))cos^{2}(x) - 3sin^{2}(x)cos(cos(x))*-sin(x)cos^{2}(x) - 3sin^{2}(x)sin(cos(x))*-2cos(x)sin(x) + 3cos(cos(x))*-sin(x)sin^{4}(x) + 3sin(cos(x))*4sin^{3}(x)cos(x) + 6*2sin(x)cos(x)cos(cos(x))cos(x) + 6sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x) + 6sin^{2}(x)cos(cos(x))*-sin(x) - 4cos(cos(x))*-sin(x)cos^{2}(x) - 4sin(cos(x))*-2cos(x)sin(x) + 4*2sin(x)cos(x)sin(cos(x)) + 4sin^{2}(x)cos(cos(x))*-sin(x)\\=&41sin(x)cos^{2}(x)cos(cos(x)) - 15sin(x)sin(cos(x))cos^{3}(x) + 4sin^{3}(x)cos^{2}(x)cos(cos(x)) + 22sin(cos(x))sin^{3}(x)cos(x) + 6sin^{3}(x)cos(cos(x))cos^{2}(x) + sin(cos(x))sin^{5}(x)cos(x) + 4sin(x)cos(cos(x))cos^{2}(x) - 20sin^{3}(x)cos(cos(x)) + 18sin^{3}(x)sin(cos(x))cos(x) - 4sin^{5}(x)cos(cos(x)) + 16sin(x)sin(cos(x))cos(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(x)cos(x)sin(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x)sin(cos(x))cos(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x)sin(cos(x))cos(x)\right)}{dx}\\=&cos(x)sin(cos(x))cos(x) + sin(x)cos(cos(x))*-sin(x)cos(x) + sin(x)sin(cos(x))*-sin(x)\\=&-sin^{2}(x)cos(cos(x))cos(x) + sin(cos(x))cos^{2}(x) - sin^{2}(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -sin^{2}(x)cos(cos(x))cos(x) + sin(cos(x))cos^{2}(x) - sin^{2}(x)sin(cos(x))\right)}{dx}\\=&-2sin(x)cos(x)cos(cos(x))cos(x) - sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x) - sin^{2}(x)cos(cos(x))*-sin(x) + cos(cos(x))*-sin(x)cos^{2}(x) + sin(cos(x))*-2cos(x)sin(x) - 2sin(x)cos(x)sin(cos(x)) - sin^{2}(x)cos(cos(x))*-sin(x)\\=&-2sin(x)cos^{2}(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)cos(x) - sin(x)cos(cos(x))cos^{2}(x) + 2sin^{3}(x)cos(cos(x)) - 4sin(x)sin(cos(x))cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2sin(x)cos^{2}(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)cos(x) - sin(x)cos(cos(x))cos^{2}(x) + 2sin^{3}(x)cos(cos(x)) - 4sin(x)sin(cos(x))cos(x)\right)}{dx}\\=&-2cos(x)cos^{2}(x)cos(cos(x)) - 2sin(x)*-2cos(x)sin(x)cos(cos(x)) - 2sin(x)cos^{2}(x)*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin^{3}(x)cos(x) - sin(cos(x))*3sin^{2}(x)cos(x)cos(x) - sin(cos(x))sin^{3}(x)*-sin(x) - cos(x)cos(cos(x))cos^{2}(x) - sin(x)*-sin(cos(x))*-sin(x)cos^{2}(x) - sin(x)cos(cos(x))*-2cos(x)sin(x) + 2*3sin^{2}(x)cos(x)cos(cos(x)) + 2sin^{3}(x)*-sin(cos(x))*-sin(x) - 4cos(x)sin(cos(x))cos(x) - 4sin(x)cos(cos(x))*-sin(x)cos(x) - 4sin(x)sin(cos(x))*-sin(x)\\=&-3cos^{3}(x)cos(cos(x)) + 10sin^{2}(x)cos(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos^{2}(x) + sin^{4}(x)cos(cos(x))cos(x) - 3sin^{2}(x)sin(cos(x))cos^{2}(x) + 3sin(cos(x))sin^{4}(x) + 6sin^{2}(x)cos(cos(x))cos(x) - 4sin(cos(x))cos^{2}(x) + 4sin^{2}(x)sin(cos(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -3cos^{3}(x)cos(cos(x)) + 10sin^{2}(x)cos(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos^{2}(x) + sin^{4}(x)cos(cos(x))cos(x) - 3sin^{2}(x)sin(cos(x))cos^{2}(x) + 3sin(cos(x))sin^{4}(x) + 6sin^{2}(x)cos(cos(x))cos(x) - 4sin(cos(x))cos^{2}(x) + 4sin^{2}(x)sin(cos(x))\right)}{dx}\\=&-3*-3cos^{2}(x)sin(x)cos(cos(x)) - 3cos^{3}(x)*-sin(cos(x))*-sin(x) + 10*2sin(x)cos(x)cos(x)cos(cos(x)) + 10sin^{2}(x)*-sin(x)cos(cos(x)) + 10sin^{2}(x)cos(x)*-sin(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)cos^{2}(x) - 3sin(cos(x))*2sin(x)cos(x)cos^{2}(x) - 3sin(cos(x))sin^{2}(x)*-2cos(x)sin(x) + 4sin^{3}(x)cos(x)cos(cos(x))cos(x) + sin^{4}(x)*-sin(cos(x))*-sin(x)cos(x) + sin^{4}(x)cos(cos(x))*-sin(x) - 3*2sin(x)cos(x)sin(cos(x))cos^{2}(x) - 3sin^{2}(x)cos(cos(x))*-sin(x)cos^{2}(x) - 3sin^{2}(x)sin(cos(x))*-2cos(x)sin(x) + 3cos(cos(x))*-sin(x)sin^{4}(x) + 3sin(cos(x))*4sin^{3}(x)cos(x) + 6*2sin(x)cos(x)cos(cos(x))cos(x) + 6sin^{2}(x)*-sin(cos(x))*-sin(x)cos(x) + 6sin^{2}(x)cos(cos(x))*-sin(x) - 4cos(cos(x))*-sin(x)cos^{2}(x) - 4sin(cos(x))*-2cos(x)sin(x) + 4*2sin(x)cos(x)sin(cos(x)) + 4sin^{2}(x)cos(cos(x))*-sin(x)\\=&41sin(x)cos^{2}(x)cos(cos(x)) - 15sin(x)sin(cos(x))cos^{3}(x) + 4sin^{3}(x)cos^{2}(x)cos(cos(x)) + 22sin(cos(x))sin^{3}(x)cos(x) + 6sin^{3}(x)cos(cos(x))cos^{2}(x) + sin(cos(x))sin^{5}(x)cos(x) + 4sin(x)cos(cos(x))cos^{2}(x) - 20sin^{3}(x)cos(cos(x)) + 18sin^{3}(x)sin(cos(x))cos(x) - 4sin^{5}(x)cos(cos(x)) + 16sin(x)sin(cos(x))cos(x)\\ \end{split}\end{equation} \]
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