There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(2{x}^{3} + 1)}{(3{x}^{2} + 7)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x^{3}}{(3x^{2} + 7)} + \frac{1}{(3x^{2} + 7)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2x^{3}}{(3x^{2} + 7)} + \frac{1}{(3x^{2} + 7)}\right)}{dx}\\=&2(\frac{-(3*2x + 0)}{(3x^{2} + 7)^{2}})x^{3} + \frac{2*3x^{2}}{(3x^{2} + 7)} + (\frac{-(3*2x + 0)}{(3x^{2} + 7)^{2}})\\=&\frac{-12x^{4}}{(3x^{2} + 7)^{2}} + \frac{6x^{2}}{(3x^{2} + 7)} - \frac{6x}{(3x^{2} + 7)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-12x^{4}}{(3x^{2} + 7)^{2}} + \frac{6x^{2}}{(3x^{2} + 7)} - \frac{6x}{(3x^{2} + 7)^{2}}\right)}{dx}\\=&-12(\frac{-2(3*2x + 0)}{(3x^{2} + 7)^{3}})x^{4} - \frac{12*4x^{3}}{(3x^{2} + 7)^{2}} + 6(\frac{-(3*2x + 0)}{(3x^{2} + 7)^{2}})x^{2} + \frac{6*2x}{(3x^{2} + 7)} - 6(\frac{-2(3*2x + 0)}{(3x^{2} + 7)^{3}})x - \frac{6}{(3x^{2} + 7)^{2}}\\=&\frac{144x^{5}}{(3x^{2} + 7)^{3}} - \frac{84x^{3}}{(3x^{2} + 7)^{2}} + \frac{12x}{(3x^{2} + 7)} + \frac{72x^{2}}{(3x^{2} + 7)^{3}} - \frac{6}{(3x^{2} + 7)^{2}}\\ \end{split}\end{equation} \]

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