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

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