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

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