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

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