There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{2}({{e}^{x}}^{2} - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}{e}^{(2x)} - x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}{e}^{(2x)} - x^{2}\right)}{dx}\\=&2x{e}^{(2x)} + x^{2}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) - 2x\\=&2x{e}^{(2x)} + 2x^{2}{e}^{(2x)} - 2x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{e}^{(2x)} + 2x^{2}{e}^{(2x)} - 2x\right)}{dx}\\=&2{e}^{(2x)} + 2x({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 2*2x{e}^{(2x)} + 2x^{2}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) - 2\\=&2{e}^{(2x)} + 8x{e}^{(2x)} + 4x^{2}{e}^{(2x)} - 2\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2{e}^{(2x)} + 8x{e}^{(2x)} + 4x^{2}{e}^{(2x)} - 2\right)}{dx}\\=&2({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 8{e}^{(2x)} + 8x({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 4*2x{e}^{(2x)} + 4x^{2}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 0\\=&12{e}^{(2x)} + 24x{e}^{(2x)} + 8x^{2}{e}^{(2x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12{e}^{(2x)} + 24x{e}^{(2x)} + 8x^{2}{e}^{(2x)}\right)}{dx}\\=&12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 24{e}^{(2x)} + 24x({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)})) + 8*2x{e}^{(2x)} + 8x^{2}({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))\\=&48{e}^{(2x)} + 64x{e}^{(2x)} + 16x^{2}{e}^{(2x)}\\ \end{split}\end{equation} \]

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