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

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