本次共计算 1 个题目：每一题对 x 求 15 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数cos(x)sin(x)tan(x) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x)cos(x)tan(x)\\\\ &\color{blue}{函数的 15 阶导数：} \\=&28556359680cos^{2}(x)tan(x)sec^{14}(x) - 28556359680sin^{2}(x)tan(x)sec^{14}(x) + 1903757312sin(x)cos(x)sec^{16}(x) + 89702612992sin(x)cos(x)tan^{2}(x)sec^{14}(x) - 9394667520sin(x)cos(x)sec^{14}(x) + 315250053120cos^{2}(x)tan^{3}(x)sec^{12}(x) - 40710225920cos^{2}(x)tan(x)sec^{12}(x) + 40710225920sin^{2}(x)tan(x)sec^{12}(x) - 334026362880sin(x)cos(x)tan^{2}(x)sec^{12}(x) - 315250053120sin^{2}(x)tan^{3}(x)sec^{12}(x) + 460858269696sin(x)cos(x)tan^{4}(x)sec^{12}(x) + 16998998016cos^{2}(x)tan(x)sec^{10}(x) - 16998998016sin^{2}(x)tan(x)sec^{10}(x) + 7726817280sin(x)cos(x)sec^{12}(x) + 197900451840sin(x)cos(x)tan^{2}(x)sec^{10}(x) - 319641620480cos^{2}(x)tan^{3}(x)sec^{10}(x) + 319641620480sin^{2}(x)tan^{3}(x)sec^{10}(x) - 1204671283200sin(x)cos(x)tan^{4}(x)sec^{10}(x) + 625974681600cos^{2}(x)tan^{5}(x)sec^{10}(x) - 625974681600sin^{2}(x)tan^{5}(x)sec^{10}(x) + 559148810240sin(x)cos(x)tan^{6}(x)sec^{10}(x) - 3268362240cos^{2}(x)tan(x)sec^{8}(x) + 3268362240sin^{2}(x)tan(x)sec^{8}(x) - 2542059520sin(x)cos(x)sec^{10}(x) - 43953029120sin(x)cos(x)tan^{2}(x)sec^{8}(x) + 88463671296cos^{2}(x)tan^{3}(x)sec^{8}(x) - 88463671296sin^{2}(x)tan^{3}(x)sec^{8}(x) + 464173731840sin(x)cos(x)tan^{4}(x)sec^{8}(x) - 913429708800sin(x)cos(x)tan^{6}(x)sec^{8}(x) - 404765204480cos^{2}(x)tan^{5}(x)sec^{8}(x) + 404765204480sin^{2}(x)tan^{5}(x)sec^{8}(x) + 182172651520sin(x)cos(x)tan^{8}(x)sec^{8}(x) + 303926476800cos^{2}(x)tan^{7}(x)sec^{8}(x) - 303926476800sin^{2}(x)tan^{7}(x)sec^{8}(x) + 4744396800sin(x)cos(x)tan^{2}(x)sec^{6}(x) - 59533393920sin(x)cos(x)tan^{4}(x)sec^{6}(x) + 348508160cos^{2}(x)tan(x)sec^{6}(x) - 348508160sin^{2}(x)tan(x)sec^{6}(x) + 448081920sin(x)cos(x)sec^{8}(x) - 10121379840cos^{2}(x)tan^{3}(x)sec^{6}(x) + 10121379840sin^{2}(x)tan^{3}(x)sec^{6}(x) + 190632099840sin(x)cos(x)tan^{6}(x)sec^{6}(x) - 150312960000sin(x)cos(x)tan^{8}(x)sec^{6}(x) + 62694567936cos^{2}(x)tan^{5}(x)sec^{6}(x) - 62694567936sin^{2}(x)tan^{5}(x)sec^{6}(x) + 13754155008sin(x)cos(x)tan^{10}(x)sec^{6}(x) - 270606336sin(x)cos(x)tan^{2}(x)sec^{4}(x) - 102867681280cos^{2}(x)tan^{7}(x)sec^{6}(x) + 102867681280sin^{2}(x)tan^{7}(x)sec^{6}(x) + 3004784640sin(x)cos(x)tan^{4}(x)sec^{4}(x) + 33464217600cos^{2}(x)tan^{9}(x)sec^{6}(x) - 33464217600sin^{2}(x)tan^{9}(x)sec^{6}(x) - 10127237120sin(x)cos(x)tan^{6}(x)sec^{4}(x) + 533012480cos^{2}(x)tan^{3}(x)sec^{4}(x) - 533012480sin^{2}(x)tan^{3}(x)sec^{4}(x) + 11327447040sin(x)cos(x)tan^{8}(x)sec^{4}(x) - 3512033280sin(x)cos(x)tan^{10}(x)sec^{4}(x) - 3162931200cos^{2}(x)tan^{5}(x)sec^{4}(x) + 3162931200sin^{2}(x)tan^{5}(x)sec^{4}(x) + 134094848sin(x)cos(x)tan^{12}(x)sec^{4}(x) + 6174744576cos^{2}(x)tan^{7}(x)sec^{4}(x) - 6174744576sin^{2}(x)tan^{7}(x)sec^{4}(x) - 3794452480cos^{2}(x)tan^{9}(x)sec^{4}(x) + 3794452480sin^{2}(x)tan^{9}(x)sec^{4}(x) - 22364160cos^{2}(x)tan(x)sec^{4}(x) + 22364160sin^{2}(x)tan(x)sec^{4}(x) - 49201152sin(x)cos(x)sec^{6}(x) + 502456320cos^{2}(x)tan^{11}(x)sec^{4}(x) - 502456320sin^{2}(x)tan^{11}(x)sec^{4}(x) + 3727360sin(x)cos(x)sec^{4}(x) - 11182080cos^{2}(x)tan^{3}(x)sec^{2}(x) + 11182080sin^{2}(x)tan^{3}(x)sec^{2}(x) - 49201152sin(x)cos(x)tan^{4}(x)sec^{2}(x) + 41000960cos^{2}(x)tan^{5}(x)sec^{2}(x) - 41000960sin^{2}(x)tan^{5}(x)sec^{2}(x) + 105431040sin(x)cos(x)tan^{6}(x)sec^{2}(x) - 52715520cos^{2}(x)tan^{7}(x)sec^{2}(x) + 52715520sin^{2}(x)tan^{7}(x)sec^{2}(x) - 82001920sin(x)cos(x)tan^{8}(x)sec^{2}(x) + 24600576cos^{2}(x)tan^{9}(x)sec^{2}(x) - 24600576sin^{2}(x)tan^{9}(x)sec^{2}(x) + 22364160sin(x)cos(x)tan^{10}(x)sec^{2}(x) - 3727360cos^{2}(x)tan^{11}(x)sec^{2}(x) + 3727360sin^{2}(x)tan^{11}(x)sec^{2}(x) - 1720320sin(x)cos(x)tan^{12}(x)sec^{2}(x) + 122880cos^{2}(x)tan^{13}(x)sec^{2}(x) + 860160cos^{2}(x)tan(x)sec^{2}(x) - 860160sin^{2}(x)tan(x)sec^{2}(x) + 7454720sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 122880sin^{2}(x)tan^{13}(x)sec^{2}(x) + 16384sin(x)cos(x)tan^{14}(x)sec^{2}(x) - 245760sin(x)cos(x)sec^{2}(x) - 16384cos^{2}(x)tan(x) + 16384sin^{2}(x)tan(x)\\ \end{split}\end{equation} \]

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