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

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