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(arctan(cot(x)) + 5) 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(arctan(cot(x)) + 5)\right)}{dx}\\=&cos(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)\\=&\frac{-cos(arctan(cot(x)) + 5)csc^{2}(x)}{(cot^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-cos(arctan(cot(x)) + 5)csc^{2}(x)}{(cot^{2}(x) + 1)}\right)}{dx}\\=&-(\frac{-(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{2}})cos(arctan(cot(x)) + 5)csc^{2}(x) - \frac{-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)csc^{2}(x)}{(cot^{2}(x) + 1)} - \frac{cos(arctan(cot(x)) + 5)*-2csc^{2}(x)cot(x)}{(cot^{2}(x) + 1)}\\=&\frac{-2cos(arctan(cot(x)) + 5)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{sin(arctan(cot(x)) + 5)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{2cos(arctan(cot(x)) + 5)cot(x)csc^{2}(x)}{(cot^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2cos(arctan(cot(x)) + 5)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{sin(arctan(cot(x)) + 5)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{2cos(arctan(cot(x)) + 5)cot(x)csc^{2}(x)}{(cot^{2}(x) + 1)}\right)}{dx}\\=&-2(\frac{-2(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{3}})cos(arctan(cot(x)) + 5)cot(x)csc^{4}(x) - \frac{2*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{2cos(arctan(cot(x)) + 5)*-csc^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{2cos(arctan(cot(x)) + 5)cot(x)*-4csc^{4}(x)cot(x)}{(cot^{2}(x) + 1)^{2}} - (\frac{-2(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{3}})sin(arctan(cot(x)) + 5)csc^{4}(x) - \frac{cos(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{sin(arctan(cot(x)) + 5)*-4csc^{4}(x)cot(x)}{(cot^{2}(x) + 1)^{2}} + 2(\frac{-(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{2}})cos(arctan(cot(x)) + 5)cot(x)csc^{2}(x) + \frac{2*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot(x)csc^{2}(x)}{(cot^{2}(x) + 1)} + \frac{2cos(arctan(cot(x)) + 5)*-csc^{2}(x)csc^{2}(x)}{(cot^{2}(x) + 1)} + \frac{2cos(arctan(cot(x)) + 5)cot(x)*-2csc^{2}(x)cot(x)}{(cot^{2}(x) + 1)}\\=&\frac{-8cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{6sin(arctan(cot(x)) + 5)cot(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{2cos(arctan(cot(x)) + 5)csc^{6}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{12cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{cos(arctan(cot(x)) + 5)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{6sin(arctan(cot(x)) + 5)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{2cos(arctan(cot(x)) + 5)csc^{4}(x)}{(cot^{2}(x) + 1)} - \frac{4cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{2}(x)}{(cot^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-8cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{6sin(arctan(cot(x)) + 5)cot(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{2cos(arctan(cot(x)) + 5)csc^{6}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{12cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{cos(arctan(cot(x)) + 5)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{6sin(arctan(cot(x)) + 5)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{2cos(arctan(cot(x)) + 5)csc^{4}(x)}{(cot^{2}(x) + 1)} - \frac{4cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{2}(x)}{(cot^{2}(x) + 1)}\right)}{dx}\\=&-8(\frac{-3(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{4}})cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{6}(x) - \frac{8*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{8cos(arctan(cot(x)) + 5)*-2cot(x)csc^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{8cos(arctan(cot(x)) + 5)cot^{2}(x)*-6csc^{6}(x)cot(x)}{(cot^{2}(x) + 1)^{3}} - 6(\frac{-3(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{4}})sin(arctan(cot(x)) + 5)cot(x)csc^{6}(x) - \frac{6cos(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{6sin(arctan(cot(x)) + 5)*-csc^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{6sin(arctan(cot(x)) + 5)cot(x)*-6csc^{6}(x)cot(x)}{(cot^{2}(x) + 1)^{3}} + 2(\frac{-2(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{3}})cos(arctan(cot(x)) + 5)csc^{6}(x) + \frac{2*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)csc^{6}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{2cos(arctan(cot(x)) + 5)*-6csc^{6}(x)cot(x)}{(cot^{2}(x) + 1)^{2}} + 12(\frac{-2(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{3}})cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{4}(x) + \frac{12*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{12cos(arctan(cot(x)) + 5)*-2cot(x)csc^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{12cos(arctan(cot(x)) + 5)cot^{2}(x)*-4csc^{4}(x)cot(x)}{(cot^{2}(x) + 1)^{2}} + (\frac{-3(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{4}})cos(arctan(cot(x)) + 5)csc^{6}(x) + \frac{-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{cos(arctan(cot(x)) + 5)*-6csc^{6}(x)cot(x)}{(cot^{2}(x) + 1)^{3}} + 6(\frac{-2(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{3}})sin(arctan(cot(x)) + 5)cot(x)csc^{4}(x) + \frac{6cos(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{6sin(arctan(cot(x)) + 5)*-csc^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{6sin(arctan(cot(x)) + 5)cot(x)*-4csc^{4}(x)cot(x)}{(cot^{2}(x) + 1)^{2}} - 2(\frac{-(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{2}})cos(arctan(cot(x)) + 5)csc^{4}(x) - \frac{2*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)csc^{4}(x)}{(cot^{2}(x) + 1)} - \frac{2cos(arctan(cot(x)) + 5)*-4csc^{4}(x)cot(x)}{(cot^{2}(x) + 1)} - 4(\frac{-(-2cot(x)csc^{2}(x) + 0)}{(cot^{2}(x) + 1)^{2}})cos(arctan(cot(x)) + 5)cot^{2}(x)csc^{2}(x) - \frac{4*-sin(arctan(cot(x)) + 5)((\frac{(-csc^{2}(x))}{(1 + (cot(x))^{2})}) + 0)cot^{2}(x)csc^{2}(x)}{(cot^{2}(x) + 1)} - \frac{4cos(arctan(cot(x)) + 5)*-2cot(x)csc^{2}(x)csc^{2}(x)}{(cot^{2}(x) + 1)} - \frac{4cos(arctan(cot(x)) + 5)cot^{2}(x)*-2csc^{2}(x)cot(x)}{(cot^{2}(x) + 1)}\\=&\frac{-48cos(arctan(cot(x)) + 5)cot^{3}(x)csc^{8}(x)}{(cot^{2}(x) + 1)^{4}} - \frac{44sin(arctan(cot(x)) + 5)cot^{2}(x)csc^{8}(x)}{(cot^{2}(x) + 1)^{4}} + \frac{24cos(arctan(cot(x)) + 5)cot(x)csc^{8}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{96cos(arctan(cot(x)) + 5)cot^{3}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{12cos(arctan(cot(x)) + 5)cot(x)csc^{8}(x)}{(cot^{2}(x) + 1)^{4}} + \frac{8sin(arctan(cot(x)) + 5)csc^{8}(x)}{(cot^{2}(x) + 1)^{3}} + \frac{72sin(arctan(cot(x)) + 5)cot^{2}(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{40cos(arctan(cot(x)) + 5)cot(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{16cos(arctan(cot(x)) + 5)cot(x)csc^{4}(x)}{(cot^{2}(x) + 1)} - \frac{56cos(arctan(cot(x)) + 5)cot^{3}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{sin(arctan(cot(x)) + 5)csc^{8}(x)}{(cot^{2}(x) + 1)^{4}} - \frac{12cos(arctan(cot(x)) + 5)cot(x)csc^{6}(x)}{(cot^{2}(x) + 1)^{3}} - \frac{8sin(arctan(cot(x)) + 5)csc^{6}(x)}{(cot^{2}(x) + 1)^{2}} - \frac{28sin(arctan(cot(x)) + 5)cot^{2}(x)csc^{4}(x)}{(cot^{2}(x) + 1)^{2}} + \frac{8cos(arctan(cot(x)) + 5)cot^{3}(x)csc^{2}(x)}{(cot^{2}(x) + 1)}\\ \end{split}\end{equation}
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