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

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