There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ cos(sin(arctan(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&\frac{420x^{2}sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{60sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{4}} - \frac{80xcos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{60xsin^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{120xsin(arctan(x))sin(sin(arctan(x)))cos^{2}(arctan(x))}{(x^{2} + 1)^{5}} + \frac{288x^{2}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{4}} - \frac{10sin(arctan(x))cos^{3}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{160xcos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{4}} + \frac{400x^{3}cos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{140x^{2}sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{5}} - \frac{400x^{3}sin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{160xsin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{4}} + \frac{140x^{2}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{384x^{4}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{15sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{24sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{3}} - \frac{10sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{5}} + \frac{3sin^{2}(arctan(x))sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} + \frac{12sin(sin(arctan(x)))sin^{2}(arctan(x))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{20sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{4}} - \frac{20xcos^{4}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{20sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{4}} + \frac{20xsin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{sin(sin(arctan(x)))cos^{5}(arctan(x))}{(x^{2} + 1)^{5}} - \frac{sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}}\\ \end{split}\end{equation} \]

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