There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({x}^{2} + x + 2)}^{(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} + x + 2)^{(x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} + x + 2)^{(x + 1)}\right)}{dx}\\=&((x^{2} + x + 2)^{(x + 1)}((1 + 0)ln(x^{2} + x + 2) + \frac{(x + 1)(2x + 1 + 0)}{(x^{2} + x + 2)}))\\=&(x^{2} + x + 2)^{(x + 1)}ln(x^{2} + x + 2) + \frac{2x^{2}(x^{2} + x + 2)^{(x + 1)}}{(x^{2} + x + 2)} + \frac{3x(x^{2} + x + 2)^{(x + 1)}}{(x^{2} + x + 2)} + \frac{(x^{2} + x + 2)^{(x + 1)}}{(x^{2} + x + 2)}\\ \end{split}\end{equation} \]

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