There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{8x}{(1 + 3{x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{8x}{(3x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{8x}{(3x^{2} + 1)}\right)}{dx}\\=&8(\frac{-(3*2x + 0)}{(3x^{2} + 1)^{2}})x + \frac{8}{(3x^{2} + 1)}\\=&\frac{-48x^{2}}{(3x^{2} + 1)^{2}} + \frac{8}{(3x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-48x^{2}}{(3x^{2} + 1)^{2}} + \frac{8}{(3x^{2} + 1)}\right)}{dx}\\=&-48(\frac{-2(3*2x + 0)}{(3x^{2} + 1)^{3}})x^{2} - \frac{48*2x}{(3x^{2} + 1)^{2}} + 8(\frac{-(3*2x + 0)}{(3x^{2} + 1)^{2}})\\=&\frac{576x^{3}}{(3x^{2} + 1)^{3}} - \frac{144x}{(3x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{576x^{3}}{(3x^{2} + 1)^{3}} - \frac{144x}{(3x^{2} + 1)^{2}}\right)}{dx}\\=&576(\frac{-3(3*2x + 0)}{(3x^{2} + 1)^{4}})x^{3} + \frac{576*3x^{2}}{(3x^{2} + 1)^{3}} - 144(\frac{-2(3*2x + 0)}{(3x^{2} + 1)^{3}})x - \frac{144}{(3x^{2} + 1)^{2}}\\=&\frac{-10368x^{4}}{(3x^{2} + 1)^{4}} + \frac{3456x^{2}}{(3x^{2} + 1)^{3}} - \frac{144}{(3x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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