本次共计算 1 个题目：每一题对 x 求 6 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(sin(sin(x))) 关于 x 的 6 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 6 阶导数：} \\=&-105sin(x)cos^{4}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 6sin(x)cos^{4}(x)cos^{5}(sin(x))cos(sin(sin(x))) - 53sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(x))) - 4sin(x)cos^{3}(sin(x))cos^{4}(x)cos(sin(sin(x))) - 44sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x)) + 28sin^{2}(sin(x))sin(x)cos^{4}(x)cos(sin(x))cos(sin(sin(x))) + 44sin(sin(x))sin(x)sin(sin(sin(x)))cos^{3}(sin(x))cos^{4}(x) + 144sin^{2}(x)sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos^{2}(sin(x)) + 34sin(sin(x))sin^{2}(x)cos^{2}(x)cos^{2}(sin(x))cos(sin(sin(x))) + 32sin^{2}(sin(x))sin(x)cos(sin(x))cos^{4}(x)cos(sin(sin(x))) + 4sin(x)sin(sin(x))sin(sin(sin(x)))cos^{3}(sin(x))cos^{4}(x) - 39sin(x)cos^{2}(x)cos(sin(sin(x)))cos^{3}(sin(x)) + 36sin(sin(x))sin(x)sin(sin(sin(x)))cos^{4}(x)cos^{3}(sin(x)) + 20sin^{2}(x)sin(sin(x))cos(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + 10sin^{2}(sin(x))sin(x)cos^{4}(x)cos(sin(sin(x)))cos(sin(x)) - 10sin(sin(x))cos^{6}(x)cos^{4}(sin(x))cos(sin(sin(x))) + 36sin^{2}(x)sin(sin(x))cos^{2}(x)cos^{2}(sin(x))cos(sin(sin(x))) - 39sin(sin(x))cos^{6}(x)cos^{2}(sin(x))cos(sin(sin(x))) + 18sin^{2}(x)sin(sin(x))cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(x))) - 10sin(x)cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 41sin(x)cos(sin(sin(x)))cos^{4}(x)cos^{3}(sin(x)) - 75sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(x))) + 54sin^{2}(sin(x))sin(x)cos(sin(sin(x)))cos^{4}(x)cos(sin(x)) - 20sin(sin(x))cos(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) + 74sin(sin(x))sin(x)sin(sin(sin(x)))cos^{2}(x)cos(sin(x)) - 26sin(x)cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x)) + 26sin(x)sin(sin(x))sin(sin(sin(x)))cos^{2}(x)cos(sin(x)) - 15sin(x)cos^{4}(x)cos(sin(x))cos(sin(sin(x))) + 56sin(sin(x))sin(x)sin(sin(sin(x)))cos^{4}(x)cos(sin(x)) + 71sin(sin(sin(x)))sin(x)sin(sin(x))cos^{2}(x)cos(sin(x)) - 6sin(sin(x))cos(sin(sin(x)))cos^{6}(x)cos^{2}(sin(x)) + 8sin(sin(x))sin^{2}(x)cos(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + 10sin(sin(x))sin^{2}(x)cos^{2}(sin(x))cos(sin(sin(x)))cos^{2}(x) + 30sin(x)sin^{2}(sin(x))cos(sin(x))cos^{4}(x)cos(sin(sin(x))) - 9sin(x)cos(sin(sin(x)))cos^{4}(x)cos^{5}(sin(x)) - 18sin(sin(x))cos^{2}(sin(x))cos^{6}(x)cos(sin(sin(x))) + 56sin(sin(x))sin(x)sin(sin(sin(x)))cos(sin(x))cos^{4}(x) + 62sin(x)sin^{2}(sin(x))cos(sin(sin(x)))cos^{4}(x)cos(sin(x)) + 9sin^{2}(sin(x))sin(x)cos(sin(x))cos(sin(sin(x)))cos^{4}(x) + 9sin^{2}(sin(x))sin(sin(sin(x)))cos^{2}(sin(x))cos^{6}(x) + 43sin(sin(sin(x)))sin^{2}(x)cos^{2}(sin(x))cos^{2}(x) + 61sin(sin(sin(x)))sin^{2}(x)cos^{2}(x)cos^{2}(sin(x)) + 34sin(sin(x))sin(sin(sin(x)))sin(x)cos(sin(x))cos^{4}(x) + 35sin(sin(sin(x)))sin(x)sin(sin(x))cos^{3}(sin(x))cos^{4}(x) + 6sin(sin(sin(x)))sin^{2}(x)cos^{4}(sin(x))cos^{2}(x) + 15sin(sin(sin(x)))sin(x)sin(sin(x))cos^{4}(x)cos^{3}(sin(x)) + 28sin(sin(x))sin(sin(sin(x)))sin(x)cos(sin(x))cos^{2}(x) - 5sin(sin(x))cos^{6}(x)cos(sin(sin(x)))cos^{4}(sin(x)) + 21sin^{2}(sin(x))sin(sin(sin(x)))cos^{6}(x)cos^{2}(sin(x)) - 12sin(sin(x))cos^{6}(x)cos(sin(sin(x)))cos^{2}(sin(x)) - 3sin(sin(x))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(x))) + 18sin(sin(sin(x)))sin(sin(x))sin(x)cos(sin(x))cos^{4}(x) + 30sin(sin(sin(x)))sin(x)sin(sin(x))cos(sin(x))cos^{4}(x) + 56sin^{2}(x)sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + 16sin(sin(x))sin(sin(sin(x)))sin(x)cos^{3}(sin(x))cos^{4}(x) + 16sin(sin(x))sin(sin(sin(x)))sin(x)cos^{4}(x)cos(sin(x)) + 2sin(sin(x))sin(x)sin(sin(sin(x)))cos(sin(x))cos^{2}(x) - sin(sin(sin(x)))cos^{6}(x)cos^{6}(sin(x)) - 9sin(sin(sin(x)))cos^{6}(x)cos^{2}(sin(x)) - 7sin(sin(sin(x)))cos^{2}(sin(x))cos^{6}(x) + 6sin(sin(sin(x)))sin^{2}(sin(x))cos^{2}(sin(x))cos^{6}(x) - 65sin(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) + 9sin(sin(sin(x)))sin^{2}(sin(x))cos^{6}(x)cos^{2}(sin(x)) + 27sin(sin(sin(x)))sin^{2}(x)cos^{2}(x)cos^{4}(sin(x)) - sin(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x) + 15sin^{3}(x)cos(sin(x))cos(sin(sin(x))) + 20sin^{2}(x)sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x) + 24sin(sin(sin(x)))sin(x)sin(sin(x))cos(sin(x))cos^{2}(x) + 15sin(sin(sin(x)))sin(x)sin(sin(x))cos^{4}(x)cos(sin(x)) - 20sin(sin(x))cos^{4}(x)cos(sin(sin(x))) + 45sin^{2}(x)sin(sin(x))cos^{2}(x)cos(sin(sin(x))) + 3sin^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 5sin(sin(sin(x)))sin(sin(x))sin^{3}(x)cos(sin(x)) - 5sin^{2}(sin(x))sin^{2}(x)sin(sin(sin(x)))cos^{2}(x) + 12sin^{3}(x)cos(sin(sin(x)))cos^{3}(sin(x)) - 16sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) - 22sin^{3}(x)sin(sin(x))sin(sin(sin(x)))cos(sin(x)) - 61sin(sin(sin(x)))sin^{2}(sin(x))sin^{2}(x)cos^{2}(x) + 12sin^{2}(x)sin(sin(sin(x)))cos^{2}(x)cos^{4}(sin(x)) - 27sin^{2}(x)sin(sin(sin(x)))sin^{2}(sin(x))cos^{2}(x) - 10sin^{3}(x)sin(sin(sin(x)))sin(sin(x))cos(sin(x)) + 6sin^{3}(sin(x))cos^{6}(x)cos(sin(sin(x))) - 20sin^{2}(x)sin^{2}(sin(x))sin(sin(sin(x)))cos^{2}(x) + 56sin^{2}(sin(x))sin(sin(sin(x)))cos^{4}(x) - 16sin(sin(x))cos^{2}(x)cos(sin(sin(x))) - 8sin(sin(sin(x)))sin^{3}(x)sin(sin(x))cos(sin(x)) - 19sin(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x)) - 22sin^{2}(sin(x))sin(sin(sin(x)))sin^{2}(x)cos^{2}(x) - 6sin(sin(sin(x)))cos^{4}(sin(x))cos^{6}(x) + 15sin^{2}(sin(x))sin(sin(sin(x)))cos^{6}(x) + 9sin^{3}(sin(x))cos(sin(sin(x)))cos^{6}(x) + 4sin(sin(sin(x)))sin^{2}(sin(x))cos^{4}(x) - 14sin(sin(sin(x)))cos^{6}(x)cos^{4}(sin(x)) - 15sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x) + 14sin^{2}(x)sin(sin(sin(x)))cos^{2}(sin(x)) - sin(sin(x))cos^{6}(x)cos(sin(sin(x))) + 15sin^{2}(x)sin(sin(x))cos(sin(sin(x))) - sin(x)cos(sin(sin(x)))cos(sin(x)) + sin(sin(sin(x)))sin^{2}(x)cos^{2}(sin(x))\\ \end{split}\end{equation} \]

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