There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{3} + 4{x}^{2} + 3x)}{(3x + 9)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(3x + 9)} + \frac{4x^{2}}{(3x + 9)} + \frac{3x}{(3x + 9)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(3x + 9)} + \frac{4x^{2}}{(3x + 9)} + \frac{3x}{(3x + 9)}\right)}{dx}\\=&(\frac{-(3 + 0)}{(3x + 9)^{2}})x^{3} + \frac{3x^{2}}{(3x + 9)} + 4(\frac{-(3 + 0)}{(3x + 9)^{2}})x^{2} + \frac{4*2x}{(3x + 9)} + 3(\frac{-(3 + 0)}{(3x + 9)^{2}})x + \frac{3}{(3x + 9)}\\=&\frac{-3x^{3}}{(3x + 9)^{2}} + \frac{3x^{2}}{(3x + 9)} - \frac{12x^{2}}{(3x + 9)^{2}} + \frac{8x}{(3x + 9)} - \frac{9x}{(3x + 9)^{2}} + \frac{3}{(3x + 9)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3x^{3}}{(3x + 9)^{2}} + \frac{3x^{2}}{(3x + 9)} - \frac{12x^{2}}{(3x + 9)^{2}} + \frac{8x}{(3x + 9)} - \frac{9x}{(3x + 9)^{2}} + \frac{3}{(3x + 9)}\right)}{dx}\\=&-3(\frac{-2(3 + 0)}{(3x + 9)^{3}})x^{3} - \frac{3*3x^{2}}{(3x + 9)^{2}} + 3(\frac{-(3 + 0)}{(3x + 9)^{2}})x^{2} + \frac{3*2x}{(3x + 9)} - 12(\frac{-2(3 + 0)}{(3x + 9)^{3}})x^{2} - \frac{12*2x}{(3x + 9)^{2}} + 8(\frac{-(3 + 0)}{(3x + 9)^{2}})x + \frac{8}{(3x + 9)} - 9(\frac{-2(3 + 0)}{(3x + 9)^{3}})x - \frac{9}{(3x + 9)^{2}} + 3(\frac{-(3 + 0)}{(3x + 9)^{2}})\\=&\frac{18x^{3}}{(3x + 9)^{3}} - \frac{18x^{2}}{(3x + 9)^{2}} + \frac{6x}{(3x + 9)} + \frac{72x^{2}}{(3x + 9)^{3}} - \frac{48x}{(3x + 9)^{2}} + \frac{54x}{(3x + 9)^{3}} - \frac{18}{(3x + 9)^{2}} + \frac{8}{(3x + 9)}\\ \end{split}\end{equation} \]

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