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

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