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

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