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

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