There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{x}{(a{x}^{2} + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(ax^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(ax^{2} + 1)}\right)}{dx}\\=&(\frac{-(a*2x + 0)}{(ax^{2} + 1)^{2}})x + \frac{1}{(ax^{2} + 1)}\\=&\frac{-2ax^{2}}{(ax^{2} + 1)^{2}} + \frac{1}{(ax^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2ax^{2}}{(ax^{2} + 1)^{2}} + \frac{1}{(ax^{2} + 1)}\right)}{dx}\\=&-2(\frac{-2(a*2x + 0)}{(ax^{2} + 1)^{3}})ax^{2} - \frac{2a*2x}{(ax^{2} + 1)^{2}} + (\frac{-(a*2x + 0)}{(ax^{2} + 1)^{2}})\\=&\frac{8a^{2}x^{3}}{(ax^{2} + 1)^{3}} - \frac{6ax}{(ax^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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