There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {e}^{(-{({x}^{2} - 1)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(-x^{4} + 2x^{2} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(-x^{4} + 2x^{2} - 1)}\right)}{dx}\\=&({e}^{(-x^{4} + 2x^{2} - 1)}((-4x^{3} + 2*2x + 0)ln(e) + \frac{(-x^{4} + 2x^{2} - 1)(0)}{(e)}))\\=&-4x^{3}{e}^{(-x^{4} + 2x^{2} - 1)} + 4x{e}^{(-x^{4} + 2x^{2} - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -4x^{3}{e}^{(-x^{4} + 2x^{2} - 1)} + 4x{e}^{(-x^{4} + 2x^{2} - 1)}\right)}{dx}\\=&-4*3x^{2}{e}^{(-x^{4} + 2x^{2} - 1)} - 4x^{3}({e}^{(-x^{4} + 2x^{2} - 1)}((-4x^{3} + 2*2x + 0)ln(e) + \frac{(-x^{4} + 2x^{2} - 1)(0)}{(e)})) + 4{e}^{(-x^{4} + 2x^{2} - 1)} + 4x({e}^{(-x^{4} + 2x^{2} - 1)}((-4x^{3} + 2*2x + 0)ln(e) + \frac{(-x^{4} + 2x^{2} - 1)(0)}{(e)}))\\=&4x^{2}{e}^{(-x^{4} + 2x^{2} - 1)} + 16x^{6}{e}^{(-x^{4} + 2x^{2} - 1)} - 32x^{4}{e}^{(-x^{4} + 2x^{2} - 1)} + 4{e}^{(-x^{4} + 2x^{2} - 1)}\\ \end{split}\end{equation} \]

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