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

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