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

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