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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(x + sin(x)) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=& - 16777216cos^{3}(x)cos(x + sin(x)) + 37277640sin^{2}(x)cos(x)cos(x + sin(x)) + 281248143sin^{2}(x)cos^{2}(x)cos(x + sin(x)) + 237535935sin(x)sin(x + sin(x))cos^{3}(x) - 63428820cos^{4}(x)cos(x + sin(x)) + 680836365sin^{2}(x)cos^{3}(x)cos(x + sin(x)) - 204804180sin^{4}(x)cos(x)cos(x + sin(x)) + 441861420sin(x)sin(x + sin(x))cos^{4}(x) - 101337600cos^{5}(x)cos(x + sin(x)) + 129156852sin^{2}(x)cos(x + sin(x))cos^{2}(x) + 420573153sin(x)sin(x + sin(x))cos^{5}(x) + 729570600sin^{2}(x)cos^{4}(x)cos(x + sin(x)) - 570817830sin^{3}(x)sin(x + sin(x))cos^{2}(x) - 373269960sin^{4}(x)cos^{2}(x)cos(x + sin(x)) + 460384848sin^{2}(x)cos^{5}(x)cos(x + sin(x)) - 801537660sin^{3}(x)sin(x + sin(x))cos^{3}(x) - 334997775sin^{4}(x)cos^{3}(x)cos(x + sin(x)) + 237045600sin^{2}(x)cos(x + sin(x))cos^{3}(x) + 118833750sin^{5}(x)sin(x + sin(x))cos^{2}(x) - 162596445sin^{3}(x)sin(x + sin(x))cos(x) + 23847390sin^{6}(x)cos(x)cos(x + sin(x)) - 127627920sin^{4}(x)cos(x + sin(x))cos(x) + 219077100sin^{2}(x)cos(x + sin(x))cos^{4}(x) - 184837590sin^{4}(x)cos(x + sin(x))cos^{2}(x) - 84342258cos^{6}(x)cos(x + sin(x)) - 520238565sin^{3}(x)sin(x + sin(x))cos^{4}(x) + 9260685sin^{6}(x)cos(x + sin(x))cos(x) + 222652430sin(x)sin(x + sin(x))cos^{6}(x) - 120685950sin^{4}(x)cos^{4}(x)cos(x + sin(x)) - 44332288cos^{7}(x)cos(x + sin(x)) + 8885520sin^{6}(x)cos^{2}(x)cos(x + sin(x)) + 82889235sin(x)sin(x + sin(x))cos^{7}(x) + 5303655sin^{6}(x)cos(x + sin(x))cos^{2}(x) + 4729725sin^{6}(x)cos^{3}(x)cos(x + sin(x)) - 228478635sin^{3}(x)sin(x + sin(x))cos^{5}(x) - 40896765sin^{4}(x)cos^{5}(x)cos(x + sin(x)) - 111172950sin^{4}(x)cos(x + sin(x))cos^{3}(x) - 44854425sin^{4}(x)cos(x + sin(x))cos^{4}(x) + 71121645sin^{5}(x)sin(x + sin(x))cos^{3}(x) + 154819665sin^{2}(x)cos^{6}(x)cos(x + sin(x)) + 121734900sin^{5}(x)sin(x + sin(x))cos(x) - 6400485sin^{4}(x)cos(x + sin(x))cos^{5}(x) - 3581865sin^{4}(x)cos^{6}(x)cos(x + sin(x)) + 43664445sin^{2}(x)cos^{7}(x)cos(x + sin(x)) - 1147860sin^{4}(x)cos(x + sin(x))cos^{6}(x) - 675675sin^{4}(x)cos^{7}(x)cos(x + sin(x)) + 108668637sin^{2}(x)cos(x + sin(x))cos^{5}(x) + 37837800sin^{2}(x)cos(x + sin(x))cos^{6}(x) + 5552910sin^{2}(x)cos^{8}(x)cos(x + sin(x)) + 17657640sin(x)sin(x + sin(x))cos^{8}(x) + 904200sin^{2}(x)cos^{9}(x)cos(x + sin(x)) + 3458455sin(x)sin(x + sin(x))cos^{9}(x) - 46569600sin^{3}(x)sin(x + sin(x))cos^{6}(x) + 6831000sin^{2}(x)cos(x + sin(x))cos^{7}(x) + 26256285sin^{2}(x)cos(x + sin(x))cos(x) + 1203840sin^{2}(x)cos(x + sin(x))cos^{8}(x) + 71775sin^{2}(x)cos(x + sin(x))cos^{9}(x) + 11868255sin^{5}(x)sin(x + sin(x))cos^{4}(x) - 9798030sin^{3}(x)sin(x + sin(x))cos^{7}(x) + 37521sin^{2}(x)cos^{10}(x)cos(x + sin(x)) + 2837835sin^{5}(x)sin(x + sin(x))cos^{5}(x) + 7524sin^{2}(x)cos(x + sin(x))cos^{10}(x) + 4095sin^{2}(x)cos^{11}(x)cos(x + sin(x)) - 2027025sin^{7}(x)sin(x + sin(x))cos(x) - 14145560cos^{8}(x)cos(x + sin(x)) + 49131810sin(x)sin(x + sin(x))cos^{2}(x) + 318318sin(x)sin(x + sin(x))cos^{10}(x) - 605385sin^{3}(x)sin(x + sin(x))cos^{8}(x) - 3615040cos^{9}(x)cos(x + sin(x)) + 38493sin(x)sin(x + sin(x))cos^{11}(x) - 58108050sin^{4}(x)cos(x + sin(x)) - 70290sin(x + sin(x))sin^{3}(x)cos^{8}(x) - 75075sin^{3}(x)sin(x + sin(x))cos^{9}(x) + 30275245sin(x + sin(x))sin(x)cos^{6}(x) + 46643310sin(x + sin(x))sin^{5}(x)cos(x) + 8288280sin(x + sin(x))sin(x)cos^{7}(x) + 18918900sin^{6}(x)cos(x + sin(x)) - 530530cos^{10}(x)cos(x + sin(x)) - 90421320sin(x + sin(x))sin^{3}(x)cos(x) + 210210sin(x + sin(x))sin(x)cos^{9}(x) + 37247175sin(x + sin(x))sin^{5}(x)cos^{2}(x) - 80080cos^{11}(x)cos(x + sin(x)) + 64354290sin(x + sin(x))sin(x)cos^{5}(x) + 27027sin(x + sin(x))sin(x)cos^{10}(x) + 57837780sin(x + sin(x))sin(x)cos^{3}(x) - 202965840sin(x + sin(x))sin^{3}(x)cos^{3}(x) + 1846845sin(x + sin(x))sin(x)cos^{8}(x) - 30394980sin(x + sin(x))sin^{3}(x)cos^{5}(x) + 16179345sin(x + sin(x))sin(x)cos^{2}(x) - 210262470sin(x + sin(x))sin^{3}(x)cos^{2}(x) + 9283680sin(x + sin(x))sin^{5}(x)cos^{3}(x) - 5460cos^{12}(x)cos(x + sin(x)) + 1092sin(x + sin(x))sin(x)cos^{11}(x) + 1274sin(x)sin(x + sin(x))cos^{12}(x) - 111968010sin(x + sin(x))sin^{3}(x)cos^{4}(x) + 2320920sin(x + sin(x))sin^{5}(x)cos^{4}(x) + 85480395sin(x + sin(x))sin(x)cos^{4}(x) - 7033950sin(x + sin(x))sin^{3}(x)cos^{6}(x) - 562320sin(x + sin(x))sin^{3}(x)cos^{7}(x) - 546cos^{13}(x)cos(x + sin(x)) + 91sin(x + sin(x))sin(x)cos^{12}(x) + 105sin(x)sin(x + sin(x))cos^{13}(x) - 1195742cos^{2}(x)cos(x + sin(x)) + 1777230sin^{2}(x)cos(x + sin(x)) + 1187550sin(x + sin(x))sin(x)cos(x) - 5591040cos(x + sin(x))cos^{3}(x) - 1768195cos(x + sin(x))cos^{8}(x) + 2383293sin(x)sin(x + sin(x))cos(x) - 14057043cos(x + sin(x))cos^{6}(x) - 640080sin(x + sin(x))sin^{7}(x) - 320320cos(x + sin(x))cos^{9}(x) - 9822483sin^{3}(x)sin(x + sin(x)) + 23196285sin(x + sin(x))sin^{5}(x) - 1386945sin^{7}(x)sin(x + sin(x)) - 53053cos(x + sin(x))cos^{10}(x) - 19987968cos(x + sin(x))cos^{5}(x) - 5857280cos(x + sin(x))cos^{7}(x) + 31668525sin^{5}(x)sin(x + sin(x)) - 15857205cos(x + sin(x))cos^{4}(x) - 4368cos(x + sin(x))cos^{11}(x) - 10763082sin(x + sin(x))sin^{3}(x) - 455cos(x + sin(x))cos^{12}(x) - 597871cos(x + sin(x))cos^{2}(x) - 14cos(x + sin(x))cos^{13}(x) - 14cos^{14}(x)cos(x + sin(x)) - 8192cos(x + sin(x))cos(x) + 8192sin(x)sin(x + sin(x)) - 8192cos(x)cos(x + sin(x)) + 8191sin(x + sin(x))sin(x) - cos(x + sin(x))cos^{14}(x) - cos^{15}(x)cos(x + sin(x)) - cos(x + sin(x))\\ \end{split}\end{equation} \]

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