There are 1 questions in this calculation: for each question, the 4 derivative of X is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{tan(X)}\ with\ respect\ to\ X：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{tan(X)}\right)}{dX}\\=&e^{tan(X)}sec^{2}(X)(1)\\=&e^{tan(X)}sec^{2}(X)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( e^{tan(X)}sec^{2}(X)\right)}{dX}\\=&e^{tan(X)}sec^{2}(X)(1)sec^{2}(X) + e^{tan(X)}*2sec^{2}(X)tan(X)\\=&e^{tan(X)}sec^{4}(X) + 2e^{tan(X)}tan(X)sec^{2}(X)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( e^{tan(X)}sec^{4}(X) + 2e^{tan(X)}tan(X)sec^{2}(X)\right)}{dX}\\=&e^{tan(X)}sec^{2}(X)(1)sec^{4}(X) + e^{tan(X)}*4sec^{4}(X)tan(X) + 2e^{tan(X)}sec^{2}(X)(1)tan(X)sec^{2}(X) + 2e^{tan(X)}sec^{2}(X)(1)sec^{2}(X) + 2e^{tan(X)}tan(X)*2sec^{2}(X)tan(X)\\=&e^{tan(X)}sec^{6}(X) + 6e^{tan(X)}tan(X)sec^{4}(X) + 2e^{tan(X)}sec^{4}(X) + 4e^{tan(X)}tan^{2}(X)sec^{2}(X)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( e^{tan(X)}sec^{6}(X) + 6e^{tan(X)}tan(X)sec^{4}(X) + 2e^{tan(X)}sec^{4}(X) + 4e^{tan(X)}tan^{2}(X)sec^{2}(X)\right)}{dX}\\=&e^{tan(X)}sec^{2}(X)(1)sec^{6}(X) + e^{tan(X)}*6sec^{6}(X)tan(X) + 6e^{tan(X)}sec^{2}(X)(1)tan(X)sec^{4}(X) + 6e^{tan(X)}sec^{2}(X)(1)sec^{4}(X) + 6e^{tan(X)}tan(X)*4sec^{4}(X)tan(X) + 2e^{tan(X)}sec^{2}(X)(1)sec^{4}(X) + 2e^{tan(X)}*4sec^{4}(X)tan(X) + 4e^{tan(X)}sec^{2}(X)(1)tan^{2}(X)sec^{2}(X) + 4e^{tan(X)}*2tan(X)sec^{2}(X)(1)sec^{2}(X) + 4e^{tan(X)}tan^{2}(X)*2sec^{2}(X)tan(X)\\=&e^{tan(X)}sec^{8}(X) + 12e^{tan(X)}tan(X)sec^{6}(X) + 28e^{tan(X)}tan^{2}(X)sec^{4}(X) + 8e^{tan(X)}sec^{6}(X) + 16e^{tan(X)}tan(X)sec^{4}(X) + 8e^{tan(X)}tan^{3}(X)sec^{2}(X)\\ \end{split}\end{equation} \]

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