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

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