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

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