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