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

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