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

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