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

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