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

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