There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ x{(a - x)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x(a - x)^{\frac{1}{2}}\right)}{dx}\\=&(a - x)^{\frac{1}{2}} + x((a - x)^{\frac{1}{2}}((0)ln(a - x) + \frac{(\frac{1}{2})(0 - 1)}{(a - x)}))\\=&\frac{-(a - x)^{\frac{1}{2}}x}{2(a - x)} + (a - x)^{\frac{1}{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-(a - x)^{\frac{1}{2}}x}{2(a - x)} + (a - x)^{\frac{1}{2}}\right)}{dx}\\=&\frac{-(\frac{\frac{1}{2}(0 - 1)}{(a - x)^{\frac{1}{2}}})x}{2(a - x)} - \frac{(a - x)^{\frac{1}{2}}(\frac{-(0 - 1)}{(a - x)^{2}})x}{2} - \frac{(a - x)^{\frac{1}{2}}}{2(a - x)} + (\frac{\frac{1}{2}(0 - 1)}{(a - x)^{\frac{1}{2}}})\\=&\frac{-x}{4(a - x)^{\frac{3}{2}}} - \frac{1}{(a - x)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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