There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {e}^{2}x + 4x{e}^{x} - {x}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xe^{2} + 4x{e}^{x} - x^{4}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xe^{2} + 4x{e}^{x} - x^{4}\right)}{dx}\\=&e^{2} + x*2e*0 + 4{e}^{x} + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 4x^{3}\\=&e^{2} + 4{e}^{x} + 4x{e}^{x} - 4x^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( e^{2} + 4{e}^{x} + 4x{e}^{x} - 4x^{3}\right)}{dx}\\=&2e*0 + 4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 4{e}^{x} + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 4*3x^{2}\\=&8{e}^{x} + 4x{e}^{x} - 12x^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8{e}^{x} + 4x{e}^{x} - 12x^{2}\right)}{dx}\\=&8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 4{e}^{x} + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 12*2x\\=&12{e}^{x} + 4x{e}^{x} - 24x\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12{e}^{x} + 4x{e}^{x} - 24x\right)}{dx}\\=&12({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 4{e}^{x} + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 24\\=&16{e}^{x} + 4x{e}^{x} - 24\\ \end{split}\end{equation} \]

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