There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {e}^{((\frac{-1}{2})({x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(\frac{-1}{2}x^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(\frac{-1}{2}x^{2})}\right)}{dx}\\=&({e}^{(\frac{-1}{2}x^{2})}((\frac{-1}{2}*2x)ln(e) + \frac{(\frac{-1}{2}x^{2})(0)}{(e)}))\\=&-x{e}^{(\frac{-1}{2}x^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -x{e}^{(\frac{-1}{2}x^{2})}\right)}{dx}\\=&-{e}^{(\frac{-1}{2}x^{2})} - x({e}^{(\frac{-1}{2}x^{2})}((\frac{-1}{2}*2x)ln(e) + \frac{(\frac{-1}{2}x^{2})(0)}{(e)}))\\=&-{e}^{(\frac{-1}{2}x^{2})} + x^{2}{e}^{(\frac{-1}{2}x^{2})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -{e}^{(\frac{-1}{2}x^{2})} + x^{2}{e}^{(\frac{-1}{2}x^{2})}\right)}{dx}\\=&-({e}^{(\frac{-1}{2}x^{2})}((\frac{-1}{2}*2x)ln(e) + \frac{(\frac{-1}{2}x^{2})(0)}{(e)})) + 2x{e}^{(\frac{-1}{2}x^{2})} + x^{2}({e}^{(\frac{-1}{2}x^{2})}((\frac{-1}{2}*2x)ln(e) + \frac{(\frac{-1}{2}x^{2})(0)}{(e)}))\\=&3x{e}^{(\frac{-1}{2}x^{2})} - x^{3}{e}^{(\frac{-1}{2}x^{2})}\\ \end{split}\end{equation} \]

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