There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {e}^{e^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{e^{x}}\right)}{dx}\\=&({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))\\=&{e}^{e^{x}}e^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {e}^{e^{x}}e^{x}\right)}{dx}\\=&({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{x} + {e}^{e^{x}}e^{x}\\=&{e}^{e^{x}}e^{{x}*{2}} + {e}^{e^{x}}e^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {e}^{e^{x}}e^{{x}*{2}} + {e}^{e^{x}}e^{x}\right)}{dx}\\=&({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{{x}*{2}} + {e}^{e^{x}}*2e^{x}e^{x} + ({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{x} + {e}^{e^{x}}e^{x}\\=&3{e}^{e^{x}}e^{{x}*{2}} + {e}^{e^{x}}e^{{x}*{3}} + {e}^{e^{x}}e^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3{e}^{e^{x}}e^{{x}*{2}} + {e}^{e^{x}}e^{{x}*{3}} + {e}^{e^{x}}e^{x}\right)}{dx}\\=&3({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{{x}*{2}} + 3{e}^{e^{x}}*2e^{x}e^{x} + ({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{{x}*{3}} + {e}^{e^{x}}*3e^{{x}*{2}}e^{x} + ({e}^{e^{x}}((e^{x})ln(e) + \frac{(e^{x})(0)}{(e)}))e^{x} + {e}^{e^{x}}e^{x}\\=&7{e}^{e^{x}}e^{{x}*{2}} + {e}^{e^{x}}e^{{x}*{4}} + 6{e}^{e^{x}}e^{{x}*{3}} + {e}^{e^{x}}e^{x}\\ \end{split}\end{equation} \]

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