There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {(1 + x)}^{(\frac{3}{2})}{\frac{1}{x}}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x + 1)^{\frac{3}{2}}}{x^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(x + 1)^{\frac{3}{2}}}{x^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(\frac{3}{2}(x + 1)^{\frac{1}{2}}(1 + 0))}{x^{\frac{1}{2}}} + \frac{(x + 1)^{\frac{3}{2}}*\frac{-1}{2}}{x^{\frac{3}{2}}}\\=&\frac{3(x + 1)^{\frac{1}{2}}}{2x^{\frac{1}{2}}} - \frac{(x + 1)^{\frac{3}{2}}}{2x^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3(x + 1)^{\frac{1}{2}}}{2x^{\frac{1}{2}}} - \frac{(x + 1)^{\frac{3}{2}}}{2x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{3(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})}{2x^{\frac{1}{2}}} + \frac{3(x + 1)^{\frac{1}{2}}*\frac{-1}{2}}{2x^{\frac{3}{2}}} - \frac{(\frac{3}{2}(x + 1)^{\frac{1}{2}}(1 + 0))}{2x^{\frac{3}{2}}} - \frac{(x + 1)^{\frac{3}{2}}*\frac{-3}{2}}{2x^{\frac{5}{2}}}\\=&\frac{3}{4(x + 1)^{\frac{1}{2}}x^{\frac{1}{2}}} - \frac{3(x + 1)^{\frac{1}{2}}}{2x^{\frac{3}{2}}} + \frac{3(x + 1)^{\frac{3}{2}}}{4x^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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