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

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