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

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