There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ 2x{{e}^{x}}^{2}(3 + 2{x}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 6x{e}^{(2x)} + 4x^{3}{e}^{(2x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 6x{e}^{(2x)} + 4x^{3}{e}^{(2x)}\right)}{dx}\\=&6{e}^{(2x)} + 6x({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 4*3x^{2}{e}^{(2x)} + 4x^{3}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))\\=&6{e}^{(2x)} + 12x{e}^{(2x)} + 12x^{2}{e}^{(2x)} + 8x^{3}{e}^{(2x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 6{e}^{(2x)} + 12x{e}^{(2x)} + 12x^{2}{e}^{(2x)} + 8x^{3}{e}^{(2x)}\right)}{dx}\\=&6({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 12{e}^{(2x)} + 12x({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 12*2x{e}^{(2x)} + 12x^{2}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 8*3x^{2}{e}^{(2x)} + 8x^{3}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))\\=&24{e}^{(2x)} + 48x{e}^{(2x)} + 48x^{2}{e}^{(2x)} + 16x^{3}{e}^{(2x)}\\ \end{split}\end{equation} \]

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