There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 + \frac{{(1 - x)}^{1}}{2})}{(1 - \frac{{(1 - x)}^{1}}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{-1}{2}x}{(\frac{1}{2}x + \frac{1}{2})} + \frac{\frac{3}{2}}{(\frac{1}{2}x + \frac{1}{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{-1}{2}x}{(\frac{1}{2}x + \frac{1}{2})} + \frac{\frac{3}{2}}{(\frac{1}{2}x + \frac{1}{2})}\right)}{dx}\\=&\frac{-1}{2}(\frac{-(\frac{1}{2} + 0)}{(\frac{1}{2}x + \frac{1}{2})^{2}})x - \frac{\frac{1}{2}}{(\frac{1}{2}x + \frac{1}{2})} + \frac{3}{2}(\frac{-(\frac{1}{2} + 0)}{(\frac{1}{2}x + \frac{1}{2})^{2}})\\=&\frac{x}{4(\frac{1}{2}x + \frac{1}{2})^{2}} - \frac{3}{4(\frac{1}{2}x + \frac{1}{2})^{2}} - \frac{1}{2(\frac{1}{2}x + \frac{1}{2})}\\ \end{split}\end{equation} \]

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