There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{1}{(x(x + 3))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{(x^{2} + 3x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{(x^{2} + 3x)}\right)}{dx}\\=&(\frac{-(2x + 3)}{(x^{2} + 3x)^{2}})\\=&\frac{-2x}{(x^{2} + 3x)^{2}} - \frac{3}{(x^{2} + 3x)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x}{(x^{2} + 3x)^{2}} - \frac{3}{(x^{2} + 3x)^{2}}\right)}{dx}\\=&-2(\frac{-2(2x + 3)}{(x^{2} + 3x)^{3}})x - \frac{2}{(x^{2} + 3x)^{2}} - 3(\frac{-2(2x + 3)}{(x^{2} + 3x)^{3}})\\=&\frac{8x^{2}}{(x^{2} + 3x)^{3}} + \frac{24x}{(x^{2} + 3x)^{3}} - \frac{2}{(x^{2} + 3x)^{2}} + \frac{18}{(x^{2} + 3x)^{3}}\\ \end{split}\end{equation} \]

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