There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{x}}\right)}{dx}\\=&e^{e^{x}}e^{x}\\=&e^{x}e^{e^{x}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( e^{x}e^{e^{x}}\right)}{dx}\\=&e^{x}e^{e^{x}} + e^{x}e^{e^{x}}e^{x}\\=&e^{x}e^{e^{x}} + e^{{x}*{2}}e^{e^{x}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( e^{x}e^{e^{x}} + e^{{x}*{2}}e^{e^{x}}\right)}{dx}\\=&e^{x}e^{e^{x}} + e^{x}e^{e^{x}}e^{x} + 2e^{x}e^{x}e^{e^{x}} + e^{{x}*{2}}e^{e^{x}}e^{x}\\=&e^{x}e^{e^{x}} + 3e^{{x}*{2}}e^{e^{x}} + e^{{x}*{3}}e^{e^{x}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( e^{x}e^{e^{x}} + 3e^{{x}*{2}}e^{e^{x}} + e^{{x}*{3}}e^{e^{x}}\right)}{dx}\\=&e^{x}e^{e^{x}} + e^{x}e^{e^{x}}e^{x} + 3*2e^{x}e^{x}e^{e^{x}} + 3e^{{x}*{2}}e^{e^{x}}e^{x} + 3e^{{x}*{2}}e^{x}e^{e^{x}} + e^{{x}*{3}}e^{e^{x}}e^{x}\\=&e^{x}e^{e^{x}} + 7e^{{x}*{2}}e^{e^{x}} + 6e^{{x}*{3}}e^{e^{x}} + e^{{x}*{4}}e^{e^{x}}\\ \end{split}\end{equation} \]

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