There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(sin(\frac{x}{2}))}^{-3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{sin^{3}(\frac{1}{2}x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{sin^{3}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{-3cos(\frac{1}{2}x)*\frac{1}{2}}{sin^{4}(\frac{1}{2}x)}\\=&\frac{-3cos(\frac{1}{2}x)}{2sin^{4}(\frac{1}{2}x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3cos(\frac{1}{2}x)}{2sin^{4}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{-3*-4cos(\frac{1}{2}x)*\frac{1}{2}cos(\frac{1}{2}x)}{2sin^{5}(\frac{1}{2}x)} - \frac{3*-sin(\frac{1}{2}x)*\frac{1}{2}}{2sin^{4}(\frac{1}{2}x)}\\=&\frac{3cos^{2}(\frac{1}{2}x)}{sin^{5}(\frac{1}{2}x)} + \frac{3}{4sin^{3}(\frac{1}{2}x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{3cos^{2}(\frac{1}{2}x)}{sin^{5}(\frac{1}{2}x)} + \frac{3}{4sin^{3}(\frac{1}{2}x)}\right)}{dx}\\=&\frac{3*-5cos(\frac{1}{2}x)*\frac{1}{2}cos^{2}(\frac{1}{2}x)}{sin^{6}(\frac{1}{2}x)} + \frac{3*-2cos(\frac{1}{2}x)sin(\frac{1}{2}x)*\frac{1}{2}}{sin^{5}(\frac{1}{2}x)} + \frac{3*-3cos(\frac{1}{2}x)*\frac{1}{2}}{4sin^{4}(\frac{1}{2}x)}\\=&\frac{-15cos^{3}(\frac{1}{2}x)}{2sin^{6}(\frac{1}{2}x)} - \frac{33cos(\frac{1}{2}x)}{8sin^{4}(\frac{1}{2}x)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！