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

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