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。
\[ \begin{equation}\begin{split}【1/1】求函数({x}^{2} + \frac{1}{x} - \frac{36{x}^{1}}{3})sin({x}^{3}) - tan({x}^{2} + 1) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}sin(x^{3}) + \frac{sin(x^{3})}{x} - 12xsin(x^{3}) - tan(x^{2} + 1)\\\\ &\color{blue}{函数的 15 阶导数：} \\=&1482030950400x^{2}cos(x^{3}) - 26676557107200x^{5}sin(x^{3}) - 99798905606400x^{8}cos(x^{3}) + 137193722265600x^{11}sin(x^{3}) + 87889728326400x^{14}cos(x^{3}) - 29620225514880x^{17}sin(x^{3}) - 5589257113440x^{20}cos(x^{3}) + 603546914880x^{23}sin(x^{3}) + 36605656080x^{26}cos(x^{3}) - 1147912560x^{29}sin(x^{3}) - 14348907x^{32}cos(x^{3}) - \frac{1307674368000sin(x^{3})}{x^{16}} + \frac{1307674368000cos(x^{3})}{x^{13}} + \frac{653837184000sin(x^{3})}{x^{10}} - \frac{217945728000cos(x^{3})}{x^{7}} - \frac{54486432000sin(x^{3})}{x^{4}} + \frac{10897286400cos(x^{3})}{x} - 245188944000x^{2}sin(x^{3}) - 3775909737600x^{5}cos(x^{3}) + 12002874483600x^{8}sin(x^{3}) + 13910094198000x^{11}cos(x^{3}) - 7397963412840x^{14}sin(x^{3}) - 2020205645640x^{17}cos(x^{3}) + 297420955650x^{20}sin(x^{3}) + 23548150710x^{23}cos(x^{3}) - 932678955x^{26}sin(x^{3}) - 14348907x^{29}cos(x^{3}) - 2092278988800xcos(x^{3}) + 82383485184000x^{4}sin(x^{3}) + 447560892979200x^{7}cos(x^{3}) - 783063433152000x^{10}sin(x^{3}) - 598457174515200x^{13}cos(x^{3}) + 231599521913760x^{16}sin(x^{3}) + 48941464572000x^{19}cos(x^{3}) - 5814942391440x^{22}sin(x^{3}) - 383020157520x^{25}cos(x^{3}) + 12914016300x^{28}sin(x^{3}) + 172186884x^{31}cos(x^{3}) - 4118136422400xtan(x^{2} + 1)sec^{8}(x^{2} + 1) - 19217969971200x^{3}sec^{10}(x^{2} + 1) - 332284900147200x^{3}tan^{2}(x^{2} + 1)sec^{8}(x^{2} + 1) - 12752938598400xtan^{3}(x^{2} + 1)sec^{6}(x^{2} + 1) - 1028099400007680x^{5}tan(x^{2} + 1)sec^{10}(x^{2} + 1) - 489571142860800x^{7}sec^{12}(x^{2} + 1) - 12538972628582400x^{7}tan^{2}(x^{2} + 1)sec^{10}(x^{2} + 1) - 450072458035200x^{3}tan^{4}(x^{2} + 1)sec^{6}(x^{2} + 1) - 5350282839982080x^{5}tan^{3}(x^{2} + 1)sec^{8}(x^{2} + 1) - 29410047649382400x^{7}tan^{4}(x^{2} + 1)sec^{8}(x^{2} + 1) - 3791767468769280x^{5}tan^{5}(x^{2} + 1)sec^{6}(x^{2} + 1) - 6878399771443200x^{9}tan(x^{2} + 1)sec^{12}(x^{2} + 1) - 750370884157440x^{11}sec^{14}(x^{2} + 1) - 26679353655951360x^{11}tan^{2}(x^{2} + 1)sec^{12}(x^{2} + 1) - 12078449845862400x^{7}tan^{6}(x^{2} + 1)sec^{6}(x^{2} + 1) - 3985293312000xtan^{5}(x^{2} + 1)sec^{4}(x^{2} + 1) - 76561912627200x^{3}tan^{6}(x^{2} + 1)sec^{4}(x^{2} + 1) - 54006648196300800x^{9}tan^{3}(x^{2} + 1)sec^{10}(x^{2} + 1) - 96219504731750400x^{11}tan^{4}(x^{2} + 1)sec^{10}(x^{2} + 1) - 373448551956480x^{5}tan^{7}(x^{2} + 1)sec^{4}(x^{2} + 1) - 68389128948940800x^{9}tan^{5}(x^{2} + 1)sec^{8}(x^{2} + 1) - 3275071778979840x^{13}tan(x^{2} + 1)sec^{14}(x^{2} + 1) - 62382319599616x^{15}sec^{16}(x^{2} + 1) - 2939375222521856x^{15}tan^{2}(x^{2} + 1)sec^{14}(x^{2} + 1) - 72957457701273600x^{11}tan^{6}(x^{2} + 1)sec^{8}(x^{2} + 1) - 717707044454400x^{7}tan^{8}(x^{2} + 1)sec^{4}(x^{2} + 1) - 17380523429068800x^{9}tan^{7}(x^{2} + 1)sec^{6}(x^{2} + 1) - 36155398092226560x^{13}tan^{3}(x^{2} + 1)sec^{12}(x^{2} + 1) - 15101403781398528x^{15}tan^{4}(x^{2} + 1)sec^{12}(x^{2} + 1) - 12005796741120000x^{11}tan^{8}(x^{2} + 1)sec^{6}(x^{2} + 1) - 641110691020800x^{9}tan^{9}(x^{2} + 1)sec^{4}(x^{2} + 1) - 71791784283340800x^{13}tan^{5}(x^{2} + 1)sec^{10}(x^{2} + 1) - 18322188213944320x^{15}tan^{6}(x^{2} + 1)sec^{10}(x^{2} + 1) - 280513122140160x^{11}tan^{10}(x^{2} + 1)sec^{4}(x^{2} + 1) - 66421555200xtan^{7}(x^{2} + 1)sec^{2}(x^{2} + 1) - 619934515200x^{3}tan^{8}(x^{2} + 1)sec^{2}(x^{2} + 1) - 34856719771238400x^{13}tan^{7}(x^{2} + 1)sec^{8}(x^{2} + 1) - 1487842836480x^{5}tan^{9}(x^{2} + 1)sec^{2}(x^{2} + 1) - 5969433445007360x^{15}tan^{8}(x^{2} + 1)sec^{8}(x^{2} + 1) - 3837944188108800x^{13}tan^{9}(x^{2} + 1)sec^{6}(x^{2} + 1) - 1416993177600x^{7}tan^{10}(x^{2} + 1)sec^{2}(x^{2} + 1) - 450696151302144x^{15}tan^{10}(x^{2} + 1)sec^{6}(x^{2} + 1) - 57625710428160x^{13}tan^{11}(x^{2} + 1)sec^{4}(x^{2} + 1) - 629774745600x^{9}tan^{11}(x^{2} + 1)sec^{2}(x^{2} + 1) - 4394019979264x^{15}tan^{12}(x^{2} + 1)sec^{4}(x^{2} + 1) - 137405399040x^{11}tan^{12}(x^{2} + 1)sec^{2}(x^{2} + 1) - 14092861440x^{13}tan^{13}(x^{2} + 1)sec^{2}(x^{2} + 1) - 536870912x^{15}tan^{14}(x^{2} + 1)sec^{2}(x^{2} + 1)\\ \end{split}\end{equation} \]

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