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

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