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

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