There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ 4{e}^{(\frac{-({(x - 6)}^{2})}{5})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}\right)}{dx}\\=&4({e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}((\frac{-1}{5}*2x + \frac{12}{5} + 0)ln(e) + \frac{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})(0)}{(e)}))\\=&\frac{-8x{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{5} + \frac{48{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{5}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-8x{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{5} + \frac{48{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{5}\right)}{dx}\\=&\frac{-8{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{5} - \frac{8x({e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}((\frac{-1}{5}*2x + \frac{12}{5} + 0)ln(e) + \frac{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})(0)}{(e)}))}{5} + \frac{48({e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}((\frac{-1}{5}*2x + \frac{12}{5} + 0)ln(e) + \frac{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})(0)}{(e)}))}{5}\\=&\frac{536{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{25} + \frac{16x^{2}{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{25} - \frac{192x{e}^{(\frac{-1}{5}x^{2} + \frac{12}{5}x - \frac{36}{5})}}{25}\\ \end{split}\end{equation} \]

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