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

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