There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 4x + 2)}{e^{x}(2x + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(2x + 2)e^{x}} + \frac{4x}{(2x + 2)e^{x}} + \frac{2}{(2x + 2)e^{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(2x + 2)e^{x}} + \frac{4x}{(2x + 2)e^{x}} + \frac{2}{(2x + 2)e^{x}}\right)}{dx}\\=&\frac{(\frac{-(2 + 0)}{(2x + 2)^{2}})x^{2}}{e^{x}} + \frac{2x}{(2x + 2)e^{x}} + \frac{x^{2}*-e^{x}}{(2x + 2)e^{{x}*{2}}} + \frac{4(\frac{-(2 + 0)}{(2x + 2)^{2}})x}{e^{x}} + \frac{4}{(2x + 2)e^{x}} + \frac{4x*-e^{x}}{(2x + 2)e^{{x}*{2}}} + \frac{2(\frac{-(2 + 0)}{(2x + 2)^{2}})}{e^{x}} + \frac{2*-e^{x}}{(2x + 2)e^{{x}*{2}}}\\=&\frac{-x^{2}}{(2x + 2)e^{x}} - \frac{2x}{(2x + 2)e^{x}} - \frac{8x}{(2x + 2)^{2}e^{x}} + \frac{2}{(2x + 2)e^{x}} - \frac{2x^{2}}{(2x + 2)^{2}e^{x}} - \frac{4}{(2x + 2)^{2}e^{x}}\\ \end{split}\end{equation} \]

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