本次共计算 1 个题目：每一题对 x 求 10 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(csc(x) + sin(30))}{sec(x)} - arccos(x) 关于 x 的 10 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{csc(x)}{sec(x)} + \frac{sin(30)}{sec(x)} - arccos(x)\\\\ &\color{blue}{函数的 10 阶导数：} \\=&-62325sec(x)csc^{9}(x) + \frac{62325tan^{2}(x)csc^{9}(x)}{sec(x)} + \frac{505210tan(x)cot(x)csc^{9}(x)}{sec(x)} + \frac{50521csc^{11}(x)}{sec(x)} + \frac{166200tan^{3}(x)cot(x)csc^{7}(x)}{sec(x)} + \frac{1073517cot^{2}(x)csc^{9}(x)}{sec(x)} - 1050sec^{5}(x)csc^{5}(x) + 3150tan^{2}(x)sec^{3}(x)csc^{5}(x) - 166200tan(x)cot(x)sec(x)csc^{7}(x) - 3150tan^{4}(x)sec(x)csc^{5}(x) + \frac{856260tan^{2}(x)cot^{2}(x)csc^{7}(x)}{sec(x)} - 856260cot^{2}(x)sec(x)csc^{7}(x) - 25620tan^{2}(x)sec(x)csc^{7}(x) + \frac{12810tan^{4}(x)csc^{7}(x)}{sec(x)} + \frac{2062760tan(x)cot^{3}(x)csc^{7}(x)}{sec(x)} + 15372tan(x)cot(x)sec^{3}(x)csc^{5}(x) + 12810sec^{3}(x)csc^{7}(x) - 30744tan^{3}(x)cot(x)sec(x)csc^{5}(x) - 201180tan^{2}(x)cot^{2}(x)sec(x)csc^{5}(x) + \frac{15372tan^{5}(x)cot(x)csc^{5}(x)}{sec(x)} + \frac{100590tan^{4}(x)cot^{2}(x)csc^{5}(x)}{sec(x)} + \frac{373320tan^{3}(x)cot^{3}(x)csc^{5}(x)}{sec(x)} + \frac{1949762cot^{4}(x)csc^{7}(x)}{sec(x)} + \frac{1050tan^{6}(x)csc^{5}(x)}{sec(x)} + 100590cot^{2}(x)sec^{3}(x)csc^{5}(x) - 373320tan(x)cot^{3}(x)sec(x)csc^{5}(x) + \frac{822150tan^{2}(x)cot^{4}(x)csc^{5}(x)}{sec(x)} - 822150cot^{4}(x)sec(x)csc^{5}(x) + \frac{1011660tan(x)cot^{5}(x)csc^{5}(x)}{sec(x)} + \frac{600tan^{7}(x)cot(x)csc^{3}(x)}{sec(x)} - 3780cot^{2}(x)sec^{5}(x)csc^{3}(x) - 600tan(x)cot(x)sec^{5}(x)csc^{3}(x) + 1800tan^{3}(x)cot(x)sec^{3}(x)csc^{3}(x) + 11340tan^{2}(x)cot^{2}(x)sec^{3}(x)csc^{3}(x) - 1800tan^{5}(x)cot(x)sec(x)csc^{3}(x) + 14616tan(x)cot^{3}(x)sec^{3}(x)csc^{3}(x) - 180tan^{6}(x)sec(x)csc^{3}(x) + \frac{45tan^{8}(x)csc^{3}(x)}{sec(x)} + \frac{3780tan^{6}(x)cot^{2}(x)csc^{3}(x)}{sec(x)} - 11340tan^{4}(x)cot^{2}(x)sec(x)csc^{3}(x) - 29232tan^{3}(x)cot^{3}(x)sec(x)csc^{3}(x) - 75180tan^{2}(x)cot^{4}(x)sec(x)csc^{3}(x) + 270tan^{4}(x)sec^{3}(x)csc^{3}(x) + \frac{14616tan^{5}(x)cot^{3}(x)csc^{3}(x)}{sec(x)} + \frac{37590tan^{4}(x)cot^{4}(x)csc^{3}(x)}{sec(x)} + \frac{65160tan^{3}(x)cot^{5}(x)csc^{3}(x)}{sec(x)} + \frac{540242cot^{6}(x)csc^{5}(x)}{sec(x)} - 180tan^{2}(x)sec^{5}(x)csc^{3}(x) + 37590cot^{4}(x)sec^{3}(x)csc^{3}(x) - sec^{9}(x)csc(x) + 5tan^{2}(x)sec^{7}(x)csc(x) - 10tan^{4}(x)sec^{5}(x)csc(x) - 65160tan(x)cot^{5}(x)sec(x)csc^{3}(x) + 10tan^{6}(x)sec^{3}(x)csc(x) + \frac{73620tan^{2}(x)cot^{6}(x)csc^{3}(x)}{sec(x)} + 45sec^{7}(x)csc^{3}(x) + \frac{49160tan(x)cot^{7}(x)csc^{3}(x)}{sec(x)} - 5tan^{8}(x)sec(x)csc(x) - 40tan^{7}(x)cot(x)sec(x)csc(x) - 73620cot^{6}(x)sec(x)csc^{3}(x) + \frac{14757cot^{8}(x)csc^{3}(x)}{sec(x)} + \frac{tan^{10}(x)csc(x)}{sec(x)} + \frac{10tan^{9}(x)cot(x)csc(x)}{sec(x)} + \frac{45tan^{8}(x)cot^{2}(x)csc(x)}{sec(x)} + 60tan^{5}(x)cot(x)sec^{3}(x)csc(x) - 180tan^{6}(x)cot^{2}(x)sec(x)csc(x) + \frac{120tan^{7}(x)cot^{3}(x)csc(x)}{sec(x)} - 40tan^{3}(x)cot(x)sec^{5}(x)csc(x) + 270tan^{4}(x)cot^{2}(x)sec^{3}(x)csc(x) - 360tan^{5}(x)cot^{3}(x)sec(x)csc(x) + \frac{210tan^{6}(x)cot^{4}(x)csc(x)}{sec(x)} + 10tan(x)cot(x)sec^{7}(x)csc(x) - 180tan^{2}(x)cot^{2}(x)sec^{5}(x)csc(x) + 360tan^{3}(x)cot^{3}(x)sec^{3}(x)csc(x) - 630tan^{4}(x)cot^{4}(x)sec(x)csc(x) + \frac{252tan^{5}(x)cot^{5}(x)csc(x)}{sec(x)} + 45cot^{2}(x)sec^{7}(x)csc(x) - 120tan(x)cot^{3}(x)sec^{5}(x)csc(x) + 630tan^{2}(x)cot^{4}(x)sec^{3}(x)csc(x) - 504tan^{3}(x)cot^{5}(x)sec(x)csc(x) + \frac{210tan^{4}(x)cot^{6}(x)csc(x)}{sec(x)} - 210cot^{4}(x)sec^{5}(x)csc(x) + 252tan(x)cot^{5}(x)sec^{3}(x)csc(x) - 420tan^{2}(x)cot^{6}(x)sec(x)csc(x) + \frac{120tan^{3}(x)cot^{7}(x)csc(x)}{sec(x)} + 210cot^{6}(x)sec^{3}(x)csc(x) - 120tan(x)cot^{7}(x)sec(x)csc(x) + \frac{45tan^{2}(x)cot^{8}(x)csc(x)}{sec(x)} - 45cot^{8}(x)sec(x)csc(x) + \frac{10tan(x)cot^{9}(x)csc(x)}{sec(x)} + \frac{cot^{10}(x)csc(x)}{sec(x)} - sin(30)sec^{9}(x) + 5sin(30)tan^{2}(x)sec^{7}(x) - 10sin(30)tan^{4}(x)sec^{5}(x) + 10sin(30)tan^{6}(x)sec^{3}(x) - 5sin(30)tan^{8}(x)sec(x) + \frac{sin(30)tan^{10}(x)}{sec(x)} + \frac{34459425x^{9}}{(-x^{2} + 1)^{\frac{19}{2}}} + \frac{72972900x^{7}}{(-x^{2} + 1)^{\frac{17}{2}}} + \frac{51081030x^{5}}{(-x^{2} + 1)^{\frac{15}{2}}} + \frac{13097700x^{3}}{(-x^{2} + 1)^{\frac{13}{2}}} + \frac{893025x}{(-x^{2} + 1)^{\frac{11}{2}}}\\ \end{split}\end{equation} \]

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