There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{2}(ax + b){{e}^{3}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ax^{3}{e^{3}}^{x} + bx^{2}{e^{3}}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ax^{3}{e^{3}}^{x} + bx^{2}{e^{3}}^{x}\right)}{dx}\\=&a*3x^{2}{e^{3}}^{x} + ax^{3}({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})})) + b*2x{e^{3}}^{x} + bx^{2}({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})}))\\=&3ax^{2}{e^{3}}^{x} + 3ax^{3}{e^{3}}^{x} + 2bx{e^{3}}^{x} + 3bx^{2}{e^{3}}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3ax^{2}{e^{3}}^{x} + 3ax^{3}{e^{3}}^{x} + 2bx{e^{3}}^{x} + 3bx^{2}{e^{3}}^{x}\right)}{dx}\\=&3a*2x{e^{3}}^{x} + 3ax^{2}({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})})) + 3a*3x^{2}{e^{3}}^{x} + 3ax^{3}({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})})) + 2b{e^{3}}^{x} + 2bx({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})})) + 3b*2x{e^{3}}^{x} + 3bx^{2}({e^{3}}^{x}((1)ln(e^{3}) + \frac{(x)(3e^{2}*0)}{(e^{3})}))\\=&6ax{e^{3}}^{x} + 18ax^{2}{e^{3}}^{x} + 9ax^{3}{e^{3}}^{x} + 2b{e^{3}}^{x} + 12bx{e^{3}}^{x} + 9bx^{2}{e^{3}}^{x}\\ \end{split}\end{equation} \]

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