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 3 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数ln({cos(x)}^{2} + sin(x)) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(cos^{2}(x) + sin(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(cos^{2}(x) + sin(x))\right)}{dx}\\=&\frac{(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))}\\=&\frac{-2sin(x)cos(x)}{(cos^{2}(x) + sin(x))} + \frac{cos(x)}{(cos^{2}(x) + sin(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2sin(x)cos(x)}{(cos^{2}(x) + sin(x))} + \frac{cos(x)}{(cos^{2}(x) + sin(x))}\right)}{dx}\\=&-2(\frac{-(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{2}})sin(x)cos(x) - \frac{2cos(x)cos(x)}{(cos^{2}(x) + sin(x))} - \frac{2sin(x)*-sin(x)}{(cos^{2}(x) + sin(x))} + (\frac{-(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{2}})cos(x) + \frac{-sin(x)}{(cos^{2}(x) + sin(x))}\\=&\frac{-4sin^{2}(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} + \frac{4sin(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{2cos^{2}(x)}{(cos^{2}(x) + sin(x))} + \frac{2sin^{2}(x)}{(cos^{2}(x) + sin(x))} - \frac{cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{sin(x)}{(cos^{2}(x) + sin(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4sin^{2}(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} + \frac{4sin(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{2cos^{2}(x)}{(cos^{2}(x) + sin(x))} + \frac{2sin^{2}(x)}{(cos^{2}(x) + sin(x))} - \frac{cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{sin(x)}{(cos^{2}(x) + sin(x))}\right)}{dx}\\=&-4(\frac{-2(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{3}})sin^{2}(x)cos^{2}(x) - \frac{4*2sin(x)cos(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{4sin^{2}(x)*-2cos(x)sin(x)}{(cos^{2}(x) + sin(x))^{2}} + 4(\frac{-2(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{3}})sin(x)cos^{2}(x) + \frac{4cos(x)cos^{2}(x)}{(cos^{2}(x) + sin(x))^{2}} + \frac{4sin(x)*-2cos(x)sin(x)}{(cos^{2}(x) + sin(x))^{2}} - 2(\frac{-(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{2}})cos^{2}(x) - \frac{2*-2cos(x)sin(x)}{(cos^{2}(x) + sin(x))} + 2(\frac{-(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{2}})sin^{2}(x) + \frac{2*2sin(x)cos(x)}{(cos^{2}(x) + sin(x))} - (\frac{-2(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{3}})cos^{2}(x) - \frac{-2cos(x)sin(x)}{(cos^{2}(x) + sin(x))^{2}} - (\frac{-(-2cos(x)sin(x) + cos(x))}{(cos^{2}(x) + sin(x))^{2}})sin(x) - \frac{cos(x)}{(cos^{2}(x) + sin(x))}\\=&\frac{-16sin^{3}(x)cos^{3}(x)}{(cos^{2}(x) + sin(x))^{3}} + \frac{24sin^{2}(x)cos^{3}(x)}{(cos^{2}(x) + sin(x))^{3}} - \frac{12sin(x)cos^{3}(x)}{(cos^{2}(x) + sin(x))^{2}} + \frac{12sin^{3}(x)cos(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{12sin(x)cos^{3}(x)}{(cos^{2}(x) + sin(x))^{3}} + \frac{6cos^{3}(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{12sin^{2}(x)cos(x)}{(cos^{2}(x) + sin(x))^{2}} + \frac{8sin(x)cos(x)}{(cos^{2}(x) + sin(x))} + \frac{2cos^{3}(x)}{(cos^{2}(x) + sin(x))^{3}} + \frac{3sin(x)cos(x)}{(cos^{2}(x) + sin(x))^{2}} - \frac{cos(x)}{(cos^{2}(x) + sin(x))}\\ \end{split}\end{equation} \]
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