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

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