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

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