There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {x}^{2}{e}^{(7x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{(7x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}{e}^{(7x)}\right)}{dx}\\=&2x{e}^{(7x)} + x^{2}({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)}))\\=&2x{e}^{(7x)} + 7x^{2}{e}^{(7x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{e}^{(7x)} + 7x^{2}{e}^{(7x)}\right)}{dx}\\=&2{e}^{(7x)} + 2x({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)})) + 7*2x{e}^{(7x)} + 7x^{2}({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)}))\\=&2{e}^{(7x)} + 28x{e}^{(7x)} + 49x^{2}{e}^{(7x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2{e}^{(7x)} + 28x{e}^{(7x)} + 49x^{2}{e}^{(7x)}\right)}{dx}\\=&2({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)})) + 28{e}^{(7x)} + 28x({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)})) + 49*2x{e}^{(7x)} + 49x^{2}({e}^{(7x)}((7)ln(e) + \frac{(7x)(0)}{(e)}))\\=&42{e}^{(7x)} + 294x{e}^{(7x)} + 343x^{2}{e}^{(7x)}\\ \end{split}\end{equation} \]

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