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

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