There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sec(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sec(x)\right)}{dx}\\=&sec(x)tan(x)\\=&tan(x)sec(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( tan(x)sec(x)\right)}{dx}\\=&sec^{2}(x)(1)sec(x) + tan(x)sec(x)tan(x)\\=&sec^{3}(x) + tan^{2}(x)sec(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sec^{3}(x) + tan^{2}(x)sec(x)\right)}{dx}\\=&3sec^{3}(x)tan(x) + 2tan(x)sec^{2}(x)(1)sec(x) + tan^{2}(x)sec(x)tan(x)\\=&5tan(x)sec^{3}(x) + tan^{3}(x)sec(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 5tan(x)sec^{3}(x) + tan^{3}(x)sec(x)\right)}{dx}\\=&5sec^{2}(x)(1)sec^{3}(x) + 5tan(x)*3sec^{3}(x)tan(x) + 3tan^{2}(x)sec^{2}(x)(1)sec(x) + tan^{3}(x)sec(x)tan(x)\\=&5sec^{5}(x) + 18tan^{2}(x)sec^{3}(x) + tan^{4}(x)sec(x)\\ \end{split}\end{equation} \]

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