There are 1 questions in this calculation: for each question, the 4 derivative of i is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{2e^{i}}\ with\ respect\ to\ i：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{2e^{i}}\right)}{di}\\=&e^{2e^{i}}*2e^{i}\\=&2e^{i}e^{2e^{i}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2e^{i}e^{2e^{i}}\right)}{di}\\=&2e^{i}e^{2e^{i}} + 2e^{i}e^{2e^{i}}*2e^{i}\\=&2e^{i}e^{2e^{i}} + 4e^{{i}*{2}}e^{2e^{i}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2e^{i}e^{2e^{i}} + 4e^{{i}*{2}}e^{2e^{i}}\right)}{di}\\=&2e^{i}e^{2e^{i}} + 2e^{i}e^{2e^{i}}*2e^{i} + 4*2e^{i}e^{i}e^{2e^{i}} + 4e^{{i}*{2}}e^{2e^{i}}*2e^{i}\\=&2e^{i}e^{2e^{i}} + 12e^{{i}*{2}}e^{2e^{i}} + 8e^{{i}*{3}}e^{2e^{i}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 2e^{i}e^{2e^{i}} + 12e^{{i}*{2}}e^{2e^{i}} + 8e^{{i}*{3}}e^{2e^{i}}\right)}{di}\\=&2e^{i}e^{2e^{i}} + 2e^{i}e^{2e^{i}}*2e^{i} + 12*2e^{i}e^{i}e^{2e^{i}} + 12e^{{i}*{2}}e^{2e^{i}}*2e^{i} + 8*3e^{{i}*{2}}e^{i}e^{2e^{i}} + 8e^{{i}*{3}}e^{2e^{i}}*2e^{i}\\=&2e^{i}e^{2e^{i}} + 28e^{{i}*{2}}e^{2e^{i}} + 48e^{{i}*{3}}e^{2e^{i}} + 16e^{{i}*{4}}e^{2e^{i}}\\ \end{split}\end{equation} \]

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