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

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