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

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