There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ cos(sec(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos(sec(x))\right)}{dx}\\=&-sin(sec(x))sec(x)tan(x)\\=&-sin(sec(x))tan(x)sec(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -sin(sec(x))tan(x)sec(x)\right)}{dx}\\=&-cos(sec(x))sec(x)tan(x)tan(x)sec(x) - sin(sec(x))sec^{2}(x)(1)sec(x) - sin(sec(x))tan(x)sec(x)tan(x)\\=&-cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -cos(sec(x))tan^{2}(x)sec^{2}(x) - sin(sec(x))sec^{3}(x) - sin(sec(x))tan^{2}(x)sec(x)\right)}{dx}\\=&--sin(sec(x))sec(x)tan(x)tan^{2}(x)sec^{2}(x) - cos(sec(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) - cos(sec(x))tan^{2}(x)*2sec^{2}(x)tan(x) - cos(sec(x))sec(x)tan(x)sec^{3}(x) - sin(sec(x))*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{2}(x)sec(x) - sin(sec(x))*2tan(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{2}(x)sec(x)tan(x)\\=&sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( sin(sec(x))tan^{3}(x)sec^{3}(x) - 3cos(sec(x))tan(x)sec^{4}(x) - 3cos(sec(x))tan^{3}(x)sec^{2}(x) - 5sin(sec(x))tan(x)sec^{3}(x) - sin(sec(x))tan^{3}(x)sec(x)\right)}{dx}\\=&cos(sec(x))sec(x)tan(x)tan^{3}(x)sec^{3}(x) + sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{3}(x) + sin(sec(x))tan^{3}(x)*3sec^{3}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan(x)sec^{4}(x) - 3cos(sec(x))sec^{2}(x)(1)sec^{4}(x) - 3cos(sec(x))tan(x)*4sec^{4}(x)tan(x) - 3*-sin(sec(x))sec(x)tan(x)tan^{3}(x)sec^{2}(x) - 3cos(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 3cos(sec(x))tan^{3}(x)*2sec^{2}(x)tan(x) - 5cos(sec(x))sec(x)tan(x)tan(x)sec^{3}(x) - 5sin(sec(x))sec^{2}(x)(1)sec^{3}(x) - 5sin(sec(x))tan(x)*3sec^{3}(x)tan(x) - cos(sec(x))sec(x)tan(x)tan^{3}(x)sec(x) - sin(sec(x))*3tan^{2}(x)sec^{2}(x)(1)sec(x) - sin(sec(x))tan^{3}(x)sec(x)tan(x)\\=&cos(sec(x))tan^{4}(x)sec^{4}(x) + 6sin(sec(x))tan^{2}(x)sec^{5}(x) + 6sin(sec(x))tan^{4}(x)sec^{3}(x) - 3cos(sec(x))sec^{6}(x) - 26cos(sec(x))tan^{2}(x)sec^{4}(x) - 7cos(sec(x))tan^{4}(x)sec^{2}(x) - 5sin(sec(x))sec^{5}(x) - 18sin(sec(x))tan^{2}(x)sec^{3}(x) - sin(sec(x))tan^{4}(x)sec(x)\\ \end{split}\end{equation} \]

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