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。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(sin(cox(x)x)x)x 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = xsqrt(xsin(cox^{3}))\\\\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{-23717560741875sin^{\frac{1}{2}}(cox^{3})}{32768x^{\frac{27}{2}}} + \frac{12168139858875cocos(cox^{3})}{32768x^{\frac{21}{2}}sin^{\frac{1}{2}}(cox^{3})} + \frac{3153615089625c^{2}o^{2}cos^{2}(cox^{3})}{32768x^{\frac{15}{2}}sin^{\frac{3}{2}}(cox^{3})} + \frac{579982528125c^{3}o^{3}cos(cox^{3})}{16384x^{\frac{9}{2}}sin^{\frac{1}{2}}(cox^{3})} + \frac{1739947584375c^{3}o^{3}cos^{3}(cox^{3})}{32768x^{\frac{9}{2}}sin^{\frac{5}{2}}(cox^{3})} + \frac{3217040701875c^{4}o^{4}cos^{2}(cox^{3})}{8192x^{\frac{3}{2}}sin^{\frac{3}{2}}(cox^{3})} + \frac{1442790359448133c^{5}o^{5}x^{\frac{3}{2}}cos(cox^{3})}{8192sin^{\frac{1}{2}}(cox^{3})} + \frac{9651122105625c^{4}o^{4}cos^{4}(cox^{3})}{32768x^{\frac{3}{2}}sin^{\frac{7}{2}}(cox^{3})} + \frac{2231977265174395c^{5}o^{5}x^{\frac{3}{2}}cos^{3}(cox^{3})}{8192sin^{\frac{5}{2}}(cox^{3})} + \frac{1458753084131509c^{6}o^{6}x^{\frac{9}{2}}cos^{2}(cox^{3})}{8192sin^{\frac{3}{2}}(cox^{3})} - \frac{3800660568175377c^{7}o^{7}x^{\frac{15}{2}}cos(cox^{3})}{4096sin^{\frac{1}{2}}(cox^{3})} + \frac{329047355755551c^{5}o^{5}x^{\frac{3}{2}}cos^{5}(cox^{3})}{32768sin^{\frac{9}{2}}(cox^{3})} - \frac{306828435828997c^{6}o^{6}x^{\frac{9}{2}}cos^{4}(cox^{3})}{16384sin^{\frac{7}{2}}(cox^{3})} - \frac{8080282743887521c^{7}o^{7}x^{\frac{15}{2}}cos^{3}(cox^{3})}{8192sin^{\frac{5}{2}}(cox^{3})} + \frac{57611907088626555c^{8}o^{8}x^{\frac{21}{2}}cos^{2}(cox^{3})}{1024sin^{\frac{3}{2}}(cox^{3})} - \frac{1853257159635239c^{9}o^{9}x^{\frac{27}{2}}cos(cox^{3})}{2048sin^{\frac{1}{2}}(cox^{3})} + \frac{118329327799941c^{6}o^{6}x^{\frac{9}{2}}cos^{6}(cox^{3})}{32768sin^{\frac{11}{2}}(cox^{3})} + \frac{336500278723471c^{7}o^{7}x^{\frac{15}{2}}cos^{5}(cox^{3})}{16384sin^{\frac{9}{2}}(cox^{3})} - \frac{4101622238758901c^{8}o^{8}x^{\frac{21}{2}}cos^{4}(cox^{3})}{4096sin^{\frac{7}{2}}(cox^{3})} - \frac{2935469934269889c^{9}o^{9}x^{\frac{27}{2}}cos^{3}(cox^{3})}{1024sin^{\frac{5}{2}}(cox^{3})} + \frac{6621675048882191c^{10}o^{10}x^{\frac{33}{2}}cos^{2}(cox^{3})}{2048sin^{\frac{3}{2}}(cox^{3})} - \frac{12084641798148665c^{11}o^{11}x^{\frac{39}{2}}cos(cox^{3})}{1024sin^{\frac{1}{2}}(cox^{3})} + \frac{374559047580251c^{7}o^{7}x^{\frac{15}{2}}cos^{7}(cox^{3})}{32768sin^{\frac{13}{2}}(cox^{3})} - \frac{4663994643186295c^{8}o^{8}x^{\frac{21}{2}}cos^{6}(cox^{3})}{4096sin^{\frac{11}{2}}(cox^{3})} + \frac{3769395541579009c^{9}o^{9}x^{\frac{27}{2}}cos^{5}(cox^{3})}{4096sin^{\frac{9}{2}}(cox^{3})} + \frac{7194508621021193c^{10}o^{10}x^{\frac{33}{2}}cos^{4}(cox^{3})}{2048sin^{\frac{7}{2}}(cox^{3})} - \frac{492515838712775c^{11}o^{11}x^{\frac{39}{2}}cos^{3}(cox^{3})}{2048sin^{\frac{5}{2}}(cox^{3})} - \frac{56743001414504541c^{12}o^{12}x^{\frac{45}{2}}cos^{2}(cox^{3})}{512sin^{\frac{3}{2}}(cox^{3})} + \frac{28262628499468335c^{13}o^{13}x^{\frac{51}{2}}cos(cox^{3})}{512sin^{\frac{1}{2}}(cox^{3})} + \frac{1094381763339575c^{8}o^{8}x^{\frac{21}{2}}cos^{8}(cox^{3})}{32768sin^{\frac{15}{2}}(cox^{3})} + \frac{2688449699449433c^{9}o^{9}x^{\frac{27}{2}}cos^{7}(cox^{3})}{4096sin^{\frac{13}{2}}(cox^{3})} - \frac{2038120303090259c^{10}o^{10}x^{\frac{33}{2}}cos^{6}(cox^{3})}{4096sin^{\frac{11}{2}}(cox^{3})} + \frac{54134711150914165c^{15}o^{15}x^{\frac{63}{2}}cos(cox^{3})}{256sin^{\frac{1}{2}}(cox^{3})} + \frac{17077608671466993c^{11}o^{11}x^{\frac{39}{2}}cos^{5}(cox^{3})}{2048sin^{\frac{9}{2}}(cox^{3})} - \frac{6671948080854115c^{12}o^{12}x^{\frac{45}{2}}cos^{4}(cox^{3})}{2048sin^{\frac{7}{2}}(cox^{3})} - \frac{35437898370460013c^{14}o^{14}x^{\frac{57}{2}}cos^{2}(cox^{3})}{512sin^{\frac{3}{2}}(cox^{3})} + \frac{5176669382460707c^{13}o^{13}x^{\frac{51}{2}}cos^{3}(cox^{3})}{512sin^{\frac{5}{2}}(cox^{3})} + \frac{9389796144257c^{9}o^{9}x^{\frac{27}{2}}cos^{9}(cox^{3})}{32768sin^{\frac{17}{2}}(cox^{3})} - \frac{58953151979215823c^{15}o^{15}x^{\frac{63}{2}}cos^{3}(cox^{3})}{512sin^{\frac{5}{2}}(cox^{3})} - \frac{214936233732865c^{10}o^{10}x^{\frac{33}{2}}cos^{8}(cox^{3})}{16384sin^{\frac{15}{2}}(cox^{3})} + \frac{5170053758764199c^{14}o^{14}x^{\frac{57}{2}}cos^{4}(cox^{3})}{1024sin^{\frac{7}{2}}(cox^{3})} - \frac{7999691546405849c^{11}o^{11}x^{\frac{39}{2}}cos^{7}(cox^{3})}{4096sin^{\frac{13}{2}}(cox^{3})} - \frac{12293366479230093c^{15}o^{15}x^{\frac{63}{2}}cos^{5}(cox^{3})}{1024sin^{\frac{9}{2}}(cox^{3})} + \frac{10435436576301159c^{12}o^{12}x^{\frac{45}{2}}cos^{6}(cox^{3})}{1024sin^{\frac{11}{2}}(cox^{3})} - \frac{6182289674204685c^{13}o^{13}x^{\frac{51}{2}}cos^{5}(cox^{3})}{2048sin^{\frac{9}{2}}(cox^{3})} - \frac{6707469005962547c^{14}o^{14}x^{\frac{57}{2}}cos^{6}(cox^{3})}{2048sin^{\frac{11}{2}}(cox^{3})} - \frac{397766045564037c^{10}o^{10}x^{\frac{33}{2}}cos^{10}(cox^{3})}{32768sin^{\frac{19}{2}}(cox^{3})} - \frac{6640892396500869c^{15}o^{15}x^{\frac{63}{2}}cos^{7}(cox^{3})}{2048sin^{\frac{13}{2}}(cox^{3})} + \frac{3666937034958451c^{13}o^{13}x^{\frac{51}{2}}cos^{7}(cox^{3})}{1024sin^{\frac{13}{2}}(cox^{3})} - \frac{1283792134374261c^{11}o^{11}x^{\frac{39}{2}}cos^{9}(cox^{3})}{16384sin^{\frac{17}{2}}(cox^{3})} + \frac{2782071244287959c^{14}o^{14}x^{\frac{57}{2}}cos^{8}(cox^{3})}{4096sin^{\frac{15}{2}}(cox^{3})} + \frac{304354424373351c^{15}o^{15}x^{\frac{63}{2}}cos^{9}(cox^{3})}{4096sin^{\frac{17}{2}}(cox^{3})} + \frac{77109860395395c^{12}o^{12}x^{\frac{45}{2}}cos^{8}(cox^{3})}{8192sin^{\frac{15}{2}}(cox^{3})} - \frac{263716980654199c^{13}o^{13}x^{\frac{51}{2}}cos^{9}(cox^{3})}{8192sin^{\frac{17}{2}}(cox^{3})} + \frac{116598810522113c^{14}o^{14}x^{\frac{57}{2}}cos^{10}(cox^{3})}{8192sin^{\frac{19}{2}}(cox^{3})} + \frac{1194286811861635c^{15}o^{15}x^{\frac{63}{2}}cos^{11}(cox^{3})}{8192sin^{\frac{21}{2}}(cox^{3})} + \frac{955998113111253c^{11}o^{11}x^{\frac{39}{2}}cos^{11}(cox^{3})}{32768sin^{\frac{21}{2}}(cox^{3})} - \frac{1851248223932981c^{12}o^{12}x^{\frac{45}{2}}cos^{10}(cox^{3})}{8192sin^{\frac{19}{2}}(cox^{3})} + \frac{1755931331025763c^{13}o^{13}x^{\frac{51}{2}}cos^{11}(cox^{3})}{8192sin^{\frac{21}{2}}(cox^{3})} + \frac{527079228204813c^{14}o^{14}x^{\frac{57}{2}}cos^{12}(cox^{3})}{16384sin^{\frac{23}{2}}(cox^{3})} + \frac{57069021028937c^{15}o^{15}x^{\frac{63}{2}}cos^{13}(cox^{3})}{16384sin^{\frac{25}{2}}(cox^{3})} - \frac{708324517474717c^{12}o^{12}x^{\frac{45}{2}}cos^{12}(cox^{3})}{32768sin^{\frac{23}{2}}(cox^{3})} - \frac{37437139381275c^{13}o^{13}x^{\frac{51}{2}}cos^{13}(cox^{3})}{32768sin^{\frac{25}{2}}(cox^{3})} - \frac{50165870359193c^{14}o^{14}x^{\frac{57}{2}}cos^{14}(cox^{3})}{32768sin^{\frac{27}{2}}(cox^{3})} + \frac{730143932352857369c^{15}o^{15}x^{\frac{63}{2}}cos^{15}(cox^{3})}{32768sin^{\frac{29}{2}}(cox^{3})} + \frac{23313200420236295c^{8}o^{8}x^{\frac{21}{2}}sin^{\frac{1}{2}}(cox^{3})}{2048} + \frac{643408140375c^{4}o^{4}sin^{\frac{1}{2}}(cox^{3})}{8192x^{\frac{3}{2}}} + \frac{12797406890837651c^{10}o^{10}x^{\frac{33}{2}}sin^{\frac{1}{2}}(cox^{3})}{1024} + \frac{781573329421455c^{6}o^{6}x^{\frac{9}{2}}sin^{\frac{1}{2}}(cox^{3})}{4096} - \frac{31952284681868963c^{12}o^{12}x^{\frac{45}{2}}sin^{\frac{1}{2}}(cox^{3})}{512} + \frac{3153615089625c^{2}o^{2}sin^{\frac{1}{2}}(cox^{3})}{16384x^{\frac{15}{2}}} - \frac{38676476748865027c^{14}o^{14}x^{\frac{57}{2}}sin^{\frac{1}{2}}(cox^{3})}{256}\\ \end{split}\end{equation} \]

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