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

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