There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{2}({e}^{(xx)} - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{x^{2}} - x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}{e}^{x^{2}} - x^{2}\right)}{dx}\\=&2x{e}^{x^{2}} + x^{2}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) - 2x\\=&2x{e}^{x^{2}} + 2x^{3}{e}^{x^{2}} - 2x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{e}^{x^{2}} + 2x^{3}{e}^{x^{2}} - 2x\right)}{dx}\\=&2{e}^{x^{2}} + 2x({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 2*3x^{2}{e}^{x^{2}} + 2x^{3}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) - 2\\=&2{e}^{x^{2}} + 10x^{2}{e}^{x^{2}} + 4x^{4}{e}^{x^{2}} - 2\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2{e}^{x^{2}} + 10x^{2}{e}^{x^{2}} + 4x^{4}{e}^{x^{2}} - 2\right)}{dx}\\=&2({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 10*2x{e}^{x^{2}} + 10x^{2}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 4*4x^{3}{e}^{x^{2}} + 4x^{4}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 0\\=&24x{e}^{x^{2}} + 36x^{3}{e}^{x^{2}} + 8x^{5}{e}^{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x{e}^{x^{2}} + 36x^{3}{e}^{x^{2}} + 8x^{5}{e}^{x^{2}}\right)}{dx}\\=&24{e}^{x^{2}} + 24x({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 36*3x^{2}{e}^{x^{2}} + 36x^{3}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 8*5x^{4}{e}^{x^{2}} + 8x^{5}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)}))\\=&24{e}^{x^{2}} + 156x^{2}{e}^{x^{2}} + 112x^{4}{e}^{x^{2}} + 16x^{6}{e}^{x^{2}}\\ \end{split}\end{equation} \]

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