There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {e}^{x}({x}^{2} + 3x - 7)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{x} + 3x{e}^{x} - 7{e}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}{e}^{x} + 3x{e}^{x} - 7{e}^{x}\right)}{dx}\\=&2x{e}^{x} + x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3{e}^{x} + 3x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 7({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&5x{e}^{x} - 4{e}^{x} + x^{2}{e}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 5x{e}^{x} - 4{e}^{x} + x^{2}{e}^{x}\right)}{dx}\\=&5{e}^{x} + 5x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 2x{e}^{x} + x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&{e}^{x} + 7x{e}^{x} + x^{2}{e}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {e}^{x} + 7x{e}^{x} + x^{2}{e}^{x}\right)}{dx}\\=&({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 7{e}^{x} + 7x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 2x{e}^{x} + x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&8{e}^{x} + 9x{e}^{x} + x^{2}{e}^{x}\\ \end{split}\end{equation} \]

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