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

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