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

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