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

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