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

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