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

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