There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2{x}^{2} + 4x + \frac{5}{2})}{e^{2x + 1}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x^{2}}{e^{2x + 1}} + \frac{4x}{e^{2x + 1}} + \frac{\frac{5}{2}}{e^{2x + 1}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2x^{2}}{e^{2x + 1}} + \frac{4x}{e^{2x + 1}} + \frac{\frac{5}{2}}{e^{2x + 1}}\right)}{dx}\\=&\frac{2*2x}{e^{2x + 1}} + \frac{2x^{2}*-e^{2x + 1}(2 + 0)}{e^{{\left(2x + 1\right)}*{2}}} + \frac{4}{e^{2x + 1}} + \frac{4x*-e^{2x + 1}(2 + 0)}{e^{{\left(2x + 1\right)}*{2}}} + \frac{\frac{5}{2}*-e^{2x + 1}(2 + 0)}{e^{{\left(2x + 1\right)}*{2}}}\\=&\frac{-4x}{e^{2x + 1}} - \frac{4x^{2}}{e^{2x + 1}} - \frac{1}{e^{2x + 1}}\\ \end{split}\end{equation} \]

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