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 5 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{x}^{6}sin({x}^{3}){\frac{1}{(1 - cos(x))}}^{3} 关于 x 的 5 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{6}sin(x^{3})}{(-cos(x) + 1)^{3}}\\\\ &\color{blue}{函数的 5 阶导数：} \\=&\frac{3600x^{6}sin^{3}(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{7}} - \frac{10800x^{5}sin^{2}(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{6}} - \frac{900x^{6}sin(x)sin(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{6}} - \frac{1800x^{8}sin^{2}(x)cos(x^{3})cos(x)}{(-cos(x) + 1)^{6}} + \frac{10800x^{4}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} - \frac{1296x^{10}sin(x^{3})sin(x)cos(x)}{(-cos(x) + 1)^{5}} + \frac{4680x^{7}sin(x)cos(x^{3})cos(x)}{(-cos(x) + 1)^{5}} + \frac{10440x^{7}sin(x)cos(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{180x^{6}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} + \frac{432x^{8}cos^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{1944x^{10}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} - \frac{3600x^{8}sin^{2}(x)cos(x)cos(x^{3})}{(-cos(x) + 1)^{6}} - \frac{720x^{8}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} + \frac{1080x^{5}sin(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{600x^{6}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{2520x^{6}sin^{5}(x)sin(x^{3})}{(-cos(x) + 1)^{8}} + \frac{10800x^{5}sin^{4}(x)sin(x^{3})}{(-cos(x) + 1)^{7}} + \frac{5400x^{8}sin^{4}(x)cos(x^{3})}{(-cos(x) + 1)^{7}} - \frac{18000x^{4}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{25200x^{7}sin^{3}(x)cos(x^{3})}{(-cos(x) + 1)^{6}} + \frac{2160x^{10}sin(x^{3})sin^{3}(x)}{(-cos(x) + 1)^{6}} + \frac{14400x^{3}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} + \frac{46080x^{6}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{12312x^{9}sin(x^{3})sin^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{108x^{8}cos(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{3240x^{10}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{3240x^{12}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{1440x^{5}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} - \frac{5400x^{2}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} - \frac{3600x^{3}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{39960x^{5}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{3258x^{6}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{8262x^{6}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{28890x^{8}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{6480x^{9}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} + \frac{1260x^{7}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{900x^{4}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{90x^{5}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{13608x^{9}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} + \frac{14580x^{11}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{486x^{12}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{162x^{10}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{36x^{8}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{108x^{10}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{9x^{8}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{3x^{6}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{324x^{12}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{972x^{14}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{17550x^{8}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{14400x^{4}cos(x^{3})}{(-cos(x) + 1)^{3}} - \frac{243x^{14}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} - \frac{19980x^{10}cos(x^{3})}{(-cos(x) + 1)^{3}} + \frac{4050x^{13}sin(x^{3})}{(-cos(x) + 1)^{3}} + \frac{720xsin(x^{3})}{(-cos(x) + 1)^{3}} - \frac{32760x^{7}sin(x^{3})}{(-cos(x) + 1)^{3}} + \frac{243x^{16}cos(x^{3})}{(-cos(x) + 1)^{3}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{x}^{6}sin({x}^{3}){\frac{1}{(1 - cos(x))}}^{3} 关于 x 的 5 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{6}sin(x^{3})}{(-cos(x) + 1)^{3}}\\\\ &\color{blue}{函数的 5 阶导数：} \\=&\frac{3600x^{6}sin^{3}(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{7}} - \frac{10800x^{5}sin^{2}(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{6}} - \frac{900x^{6}sin(x)sin(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{6}} - \frac{1800x^{8}sin^{2}(x)cos(x^{3})cos(x)}{(-cos(x) + 1)^{6}} + \frac{10800x^{4}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} - \frac{1296x^{10}sin(x^{3})sin(x)cos(x)}{(-cos(x) + 1)^{5}} + \frac{4680x^{7}sin(x)cos(x^{3})cos(x)}{(-cos(x) + 1)^{5}} + \frac{10440x^{7}sin(x)cos(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{180x^{6}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} + \frac{432x^{8}cos^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{1944x^{10}sin(x)sin(x^{3})cos(x)}{(-cos(x) + 1)^{5}} - \frac{3600x^{8}sin^{2}(x)cos(x)cos(x^{3})}{(-cos(x) + 1)^{6}} - \frac{720x^{8}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} + \frac{1080x^{5}sin(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{600x^{6}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{2520x^{6}sin^{5}(x)sin(x^{3})}{(-cos(x) + 1)^{8}} + \frac{10800x^{5}sin^{4}(x)sin(x^{3})}{(-cos(x) + 1)^{7}} + \frac{5400x^{8}sin^{4}(x)cos(x^{3})}{(-cos(x) + 1)^{7}} - \frac{18000x^{4}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{25200x^{7}sin^{3}(x)cos(x^{3})}{(-cos(x) + 1)^{6}} + \frac{2160x^{10}sin(x^{3})sin^{3}(x)}{(-cos(x) + 1)^{6}} + \frac{14400x^{3}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} + \frac{46080x^{6}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{12312x^{9}sin(x^{3})sin^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{108x^{8}cos(x^{3})cos^{2}(x)}{(-cos(x) + 1)^{5}} + \frac{3240x^{10}sin^{3}(x)sin(x^{3})}{(-cos(x) + 1)^{6}} - \frac{3240x^{12}sin^{2}(x)cos(x^{3})}{(-cos(x) + 1)^{5}} - \frac{1440x^{5}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} - \frac{5400x^{2}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} - \frac{3600x^{3}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{39960x^{5}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{3258x^{6}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{8262x^{6}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{28890x^{8}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{6480x^{9}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} + \frac{1260x^{7}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{900x^{4}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{90x^{5}sin(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{13608x^{9}sin^{2}(x)sin(x^{3})}{(-cos(x) + 1)^{5}} + \frac{14580x^{11}sin(x)cos(x^{3})}{(-cos(x) + 1)^{4}} + \frac{486x^{12}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{162x^{10}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{36x^{8}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{108x^{10}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{9x^{8}cos(x^{3})cos(x)}{(-cos(x) + 1)^{4}} - \frac{3x^{6}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{324x^{12}cos(x)cos(x^{3})}{(-cos(x) + 1)^{4}} - \frac{972x^{14}sin(x^{3})sin(x)}{(-cos(x) + 1)^{4}} + \frac{17550x^{8}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} + \frac{14400x^{4}cos(x^{3})}{(-cos(x) + 1)^{3}} - \frac{243x^{14}sin(x)sin(x^{3})}{(-cos(x) + 1)^{4}} - \frac{19980x^{10}cos(x^{3})}{(-cos(x) + 1)^{3}} + \frac{4050x^{13}sin(x^{3})}{(-cos(x) + 1)^{3}} + \frac{720xsin(x^{3})}{(-cos(x) + 1)^{3}} - \frac{32760x^{7}sin(x^{3})}{(-cos(x) + 1)^{3}} + \frac{243x^{16}cos(x^{3})}{(-cos(x) + 1)^{3}}\\ \end{split}\end{equation} \]
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