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

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