There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{2}{(tan(\frac{x}{2}) - 1)} + 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{2}{(tan(\frac{1}{2}x) - 1)} + 1)\right)}{dx}\\=&\frac{(2(\frac{-(sec^{2}(\frac{1}{2}x)(\frac{1}{2}) + 0)}{(tan(\frac{1}{2}x) - 1)^{2}}) + 0)}{(\frac{2}{(tan(\frac{1}{2}x) - 1)} + 1)}\\=&\frac{-sec^{2}(\frac{1}{2}x)}{(\frac{2}{(tan(\frac{1}{2}x) - 1)} + 1)(tan(\frac{1}{2}x) - 1)^{2}}\\ \end{split}\end{equation} \]

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