There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ cos(sin(x)) - cos(sin(tan(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos(sin(x)) - cos(sin(tan(x)))\right)}{dx}\\=&-sin(sin(x))cos(x) - -sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)\\=&sin(sin(tan(x)))cos(tan(x))sec^{2}(x) - sin(sin(x))cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sin(sin(tan(x)))cos(tan(x))sec^{2}(x) - sin(sin(x))cos(x)\right)}{dx}\\=&cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos(tan(x))sec^{2}(x) + sin(sin(tan(x)))*-sin(tan(x))sec^{2}(x)(1)sec^{2}(x) + sin(sin(tan(x)))cos(tan(x))*2sec^{2}(x)tan(x) - cos(sin(x))cos(x)cos(x) - sin(sin(x))*-sin(x)\\=&cos(sin(tan(x)))cos^{2}(tan(x))sec^{4}(x) - sin(sin(tan(x)))sin(tan(x))sec^{4}(x) + 2sin(sin(tan(x)))cos(tan(x))tan(x)sec^{2}(x) - cos^{2}(x)cos(sin(x)) + sin(x)sin(sin(x))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( cos(sin(tan(x)))cos^{2}(tan(x))sec^{4}(x) - sin(sin(tan(x)))sin(tan(x))sec^{4}(x) + 2sin(sin(tan(x)))cos(tan(x))tan(x)sec^{2}(x) - cos^{2}(x)cos(sin(x)) + sin(x)sin(sin(x))\right)}{dx}\\=&-sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos^{2}(tan(x))sec^{4}(x) + cos(sin(tan(x)))*-2cos(tan(x))sin(tan(x))sec^{2}(x)(1)sec^{4}(x) + cos(sin(tan(x)))cos^{2}(tan(x))*4sec^{4}(x)tan(x) - cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)sin(tan(x))sec^{4}(x) - sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)sec^{4}(x) - sin(sin(tan(x)))sin(tan(x))*4sec^{4}(x)tan(x) + 2cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos(tan(x))tan(x)sec^{2}(x) + 2sin(sin(tan(x)))*-sin(tan(x))sec^{2}(x)(1)tan(x)sec^{2}(x) + 2sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)sec^{2}(x) + 2sin(sin(tan(x)))cos(tan(x))tan(x)*2sec^{2}(x)tan(x) - -2cos(x)sin(x)cos(sin(x)) - cos^{2}(x)*-sin(sin(x))cos(x) + cos(x)sin(sin(x)) + sin(x)cos(sin(x))cos(x)\\=& - sin(sin(tan(x)))cos^{3}(tan(x))sec^{6}(x) - 3sin(tan(x))cos(tan(x))cos(sin(tan(x)))sec^{6}(x) + 6cos(sin(tan(x)))cos^{2}(tan(x))tan(x)sec^{4}(x) - sin(sin(tan(x)))cos(tan(x))sec^{6}(x) - 6sin(sin(tan(x)))sin(tan(x))tan(x)sec^{4}(x) + 2sin(sin(tan(x)))cos(tan(x))sec^{4}(x) + 4sin(sin(tan(x)))cos(tan(x))tan^{2}(x)sec^{2}(x) + 3sin(x)cos(x)cos(sin(x)) + sin(sin(x))cos^{3}(x) + sin(sin(x))cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - sin(sin(tan(x)))cos^{3}(tan(x))sec^{6}(x) - 3sin(tan(x))cos(tan(x))cos(sin(tan(x)))sec^{6}(x) + 6cos(sin(tan(x)))cos^{2}(tan(x))tan(x)sec^{4}(x) - sin(sin(tan(x)))cos(tan(x))sec^{6}(x) - 6sin(sin(tan(x)))sin(tan(x))tan(x)sec^{4}(x) + 2sin(sin(tan(x)))cos(tan(x))sec^{4}(x) + 4sin(sin(tan(x)))cos(tan(x))tan^{2}(x)sec^{2}(x) + 3sin(x)cos(x)cos(sin(x)) + sin(sin(x))cos^{3}(x) + sin(sin(x))cos(x)\right)}{dx}\\=& - cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos^{3}(tan(x))sec^{6}(x) - sin(sin(tan(x)))*-3cos^{2}(tan(x))sin(tan(x))sec^{2}(x)(1)sec^{6}(x) - sin(sin(tan(x)))cos^{3}(tan(x))*6sec^{6}(x)tan(x) - 3cos(tan(x))sec^{2}(x)(1)cos(tan(x))cos(sin(tan(x)))sec^{6}(x) - 3sin(tan(x))*-sin(tan(x))sec^{2}(x)(1)cos(sin(tan(x)))sec^{6}(x) - 3sin(tan(x))cos(tan(x))*-sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)sec^{6}(x) - 3sin(tan(x))cos(tan(x))cos(sin(tan(x)))*6sec^{6}(x)tan(x) + 6*-sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos^{2}(tan(x))tan(x)sec^{4}(x) + 6cos(sin(tan(x)))*-2cos(tan(x))sin(tan(x))sec^{2}(x)(1)tan(x)sec^{4}(x) + 6cos(sin(tan(x)))cos^{2}(tan(x))sec^{2}(x)(1)sec^{4}(x) + 6cos(sin(tan(x)))cos^{2}(tan(x))tan(x)*4sec^{4}(x)tan(x) - cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos(tan(x))sec^{6}(x) - sin(sin(tan(x)))*-sin(tan(x))sec^{2}(x)(1)sec^{6}(x) - sin(sin(tan(x)))cos(tan(x))*6sec^{6}(x)tan(x) - 6cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)sin(tan(x))tan(x)sec^{4}(x) - 6sin(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)tan(x)sec^{4}(x) - 6sin(sin(tan(x)))sin(tan(x))sec^{2}(x)(1)sec^{4}(x) - 6sin(sin(tan(x)))sin(tan(x))tan(x)*4sec^{4}(x)tan(x) + 2cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos(tan(x))sec^{4}(x) + 2sin(sin(tan(x)))*-sin(tan(x))sec^{2}(x)(1)sec^{4}(x) + 2sin(sin(tan(x)))cos(tan(x))*4sec^{4}(x)tan(x) + 4cos(sin(tan(x)))cos(tan(x))sec^{2}(x)(1)cos(tan(x))tan^{2}(x)sec^{2}(x) + 4sin(sin(tan(x)))*-sin(tan(x))sec^{2}(x)(1)tan^{2}(x)sec^{2}(x) + 4sin(sin(tan(x)))cos(tan(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4sin(sin(tan(x)))cos(tan(x))tan^{2}(x)*2sec^{2}(x)tan(x) + 3cos(x)cos(x)cos(sin(x)) + 3sin(x)*-sin(x)cos(sin(x)) + 3sin(x)cos(x)*-sin(sin(x))cos(x) + cos(sin(x))cos(x)cos^{3}(x) + sin(sin(x))*-3cos^{2}(x)sin(x) + cos(sin(x))cos(x)cos(x) + sin(sin(x))*-sin(x)\\=& - cos(sin(tan(x)))cos^{4}(tan(x))sec^{8}(x) + 6sin(sin(tan(x)))sin(tan(x))cos^{2}(tan(x))sec^{8}(x) - 12sin(sin(tan(x)))cos(tan(x))tan(x)sec^{6}(x) - 3cos^{2}(tan(x))cos(sin(tan(x)))sec^{8}(x) + 3sin^{2}(tan(x))cos(sin(tan(x)))sec^{8}(x) - 36sin(tan(x))cos(tan(x))cos(sin(tan(x)))tan(x)sec^{6}(x) - 12sin(sin(tan(x)))cos^{3}(tan(x))tan(x)sec^{6}(x) + 6cos^{2}(tan(x))cos(sin(tan(x)))sec^{6}(x) + 28cos(sin(tan(x)))cos^{2}(tan(x))tan^{2}(x)sec^{4}(x) - cos(sin(tan(x)))cos^{2}(tan(x))sec^{8}(x) + sin(sin(tan(x)))sin(tan(x))sec^{8}(x) + 16sin(sin(tan(x)))cos(tan(x))tan(x)sec^{4}(x) - 6sin(tan(x))sin(sin(tan(x)))sec^{6}(x) - 28sin(sin(tan(x)))sin(tan(x))tan^{2}(x)sec^{4}(x) + 2cos(sin(tan(x)))cos^{2}(tan(x))sec^{6}(x) - 2sin(sin(tan(x)))sin(tan(x))sec^{6}(x) + 8sin(sin(tan(x)))cos(tan(x))tan^{3}(x)sec^{2}(x) + 4cos^{2}(x)cos(sin(x)) - 3sin^{2}(x)cos(sin(x)) - 6sin(x)sin(sin(x))cos^{2}(x) + cos^{4}(x)cos(sin(x)) - sin(x)sin(sin(x))\\ \end{split}\end{equation} \]

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