There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 4x + 2)}{({e}^{x}(2x + 2))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(2x{e}^{x} + 2{e}^{x})} + \frac{4x}{(2x{e}^{x} + 2{e}^{x})} + \frac{2}{(2x{e}^{x} + 2{e}^{x})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(2x{e}^{x} + 2{e}^{x})} + \frac{4x}{(2x{e}^{x} + 2{e}^{x})} + \frac{2}{(2x{e}^{x} + 2{e}^{x})}\right)}{dx}\\=&(\frac{-(2{e}^{x} + 2x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(2x{e}^{x} + 2{e}^{x})^{2}})x^{2} + \frac{2x}{(2x{e}^{x} + 2{e}^{x})} + 4(\frac{-(2{e}^{x} + 2x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(2x{e}^{x} + 2{e}^{x})^{2}})x + \frac{4}{(2x{e}^{x} + 2{e}^{x})} + 2(\frac{-(2{e}^{x} + 2x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})))}{(2x{e}^{x} + 2{e}^{x})^{2}})\\=&\frac{-12x^{2}{e}^{x}}{(2x{e}^{x} + 2{e}^{x})^{2}} - \frac{20x{e}^{x}}{(2x{e}^{x} + 2{e}^{x})^{2}} - \frac{2x^{3}{e}^{x}}{(2x{e}^{x} + 2{e}^{x})^{2}} + \frac{2x}{(2x{e}^{x} + 2{e}^{x})} - \frac{8{e}^{x}}{(2x{e}^{x} + 2{e}^{x})^{2}} + \frac{4}{(2x{e}^{x} + 2{e}^{x})}\\ \end{split}\end{equation} \]

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