There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {(e^{2x} - ln(x + 1))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - 2e^{2x}ln(x + 1) + e^{{2x}*{2}} + ln^{2}(x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - 2e^{2x}ln(x + 1) + e^{{2x}*{2}} + ln^{2}(x + 1)\right)}{dx}\\=& - 2e^{2x}*2ln(x + 1) - \frac{2e^{2x}(1 + 0)}{(x + 1)} + 2e^{2x}e^{2x}*2 + \frac{2ln(x + 1)(1 + 0)}{(x + 1)}\\=& - 4e^{2x}ln(x + 1) - \frac{2e^{2x}}{(x + 1)} + 4e^{{2x}*{2}} + \frac{2ln(x + 1)}{(x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 4e^{2x}ln(x + 1) - \frac{2e^{2x}}{(x + 1)} + 4e^{{2x}*{2}} + \frac{2ln(x + 1)}{(x + 1)}\right)}{dx}\\=& - 4e^{2x}*2ln(x + 1) - \frac{4e^{2x}(1 + 0)}{(x + 1)} - 2(\frac{-(1 + 0)}{(x + 1)^{2}})e^{2x} - \frac{2e^{2x}*2}{(x + 1)} + 4*2e^{2x}e^{2x}*2 + 2(\frac{-(1 + 0)}{(x + 1)^{2}})ln(x + 1) + \frac{2(1 + 0)}{(x + 1)(x + 1)}\\=& - 8e^{2x}ln(x + 1) - \frac{8e^{2x}}{(x + 1)} + \frac{2e^{2x}}{(x + 1)^{2}} + 16e^{{2x}*{2}} - \frac{2ln(x + 1)}{(x + 1)^{2}} + \frac{2}{(x + 1)^{2}}\\ \end{split}\end{equation} \]

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