There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{x}{(2(2 + {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(2x^{2} + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(2x^{2} + 4)}\right)}{dx}\\=&(\frac{-(2*2x + 0)}{(2x^{2} + 4)^{2}})x + \frac{1}{(2x^{2} + 4)}\\=&\frac{-4x^{2}}{(2x^{2} + 4)^{2}} + \frac{1}{(2x^{2} + 4)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4x^{2}}{(2x^{2} + 4)^{2}} + \frac{1}{(2x^{2} + 4)}\right)}{dx}\\=&-4(\frac{-2(2*2x + 0)}{(2x^{2} + 4)^{3}})x^{2} - \frac{4*2x}{(2x^{2} + 4)^{2}} + (\frac{-(2*2x + 0)}{(2x^{2} + 4)^{2}})\\=&\frac{32x^{3}}{(2x^{2} + 4)^{3}} - \frac{12x}{(2x^{2} + 4)^{2}}\\ \end{split}\end{equation} \]

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