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

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