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

Your problem has not been solved here? Please take a look at the  hot problems ！