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。
\[ \begin{equation}\begin{split}【1/1】求函数{(sin(\frac{x}{2}))}^{-3} 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{sin^{3}(\frac{1}{2}x)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{sin^{3}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{-3cos(\frac{1}{2}x)*\frac{1}{2}}{sin^{4}(\frac{1}{2}x)}\\=&\frac{-3cos(\frac{1}{2}x)}{2sin^{4}(\frac{1}{2}x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-3cos(\frac{1}{2}x)}{2sin^{4}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{-3*-4cos(\frac{1}{2}x)*\frac{1}{2}cos(\frac{1}{2}x)}{2sin^{5}(\frac{1}{2}x)} - \frac{3*-sin(\frac{1}{2}x)*\frac{1}{2}}{2sin^{4}(\frac{1}{2}x)}\\=&\frac{3cos^{2}(\frac{1}{2}x)}{sin^{5}(\frac{1}{2}x)} + \frac{3}{4sin^{3}(\frac{1}{2}x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{3cos^{2}(\frac{1}{2}x)}{sin^{5}(\frac{1}{2}x)} + \frac{3}{4sin^{3}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{3*-5cos(\frac{1}{2}x)*\frac{1}{2}cos^{2}(\frac{1}{2}x)}{sin^{6}(\frac{1}{2}x)} + \frac{3*-2cos(\frac{1}{2}x)sin(\frac{1}{2}x)*\frac{1}{2}}{sin^{5}(\frac{1}{2}x)} + \frac{3*-3cos(\frac{1}{2}x)*\frac{1}{2}}{4sin^{4}(\frac{1}{2}x)}\\=&\frac{-15cos^{3}(\frac{1}{2}x)}{2sin^{6}(\frac{1}{2}x)} - \frac{33cos(\frac{1}{2}x)}{8sin^{4}(\frac{1}{2}x)}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！