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

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