求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数arccos(x + 3) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{-213458046676875x^{14}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{8965237960428750x^{13}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{719432675836875x^{12}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{174822140228360625x^{12}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{25899576330127500x^{11}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2097865682740327500x^{11}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{949651132104675x^{10}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{427343009447103750x^{10}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{8084019845752926067x^{10}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{28489533963140250x^{9}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{4273430094471037500x^{9}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2387258890243677362x^{9}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{619337694850875x^{8}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{384608708502393375x^{8}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{8047835009739600107x^{8}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{6130978987669160225x^{8}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{14864104676421000x^{7}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{3076869668019147000x^{7}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{9114817528814797928x^{7}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{2696742994189445592x^{7}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{206445898283625x^{6}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{156073099102420500x^{6}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{2293178316609029866x^{6}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{4991626796567310484x^{6}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{9061950704748562985x^{6}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{3716026169105250x^{5}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{936438594614523000x^{5}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{2812604504433223452x^{5}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{8246381464494974888x^{5}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{322842664212425646x^{5}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{32596720781625x^{4}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{27870196268289375x^{4}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{3511644729804461250x^{4}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{2191860775771717178x^{4}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{2984778827781473701x^{4}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{8739108040536137339x^{4}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{391160649379500x^{3}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{111480785073157500x^{3}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{8427947351530707000x^{3}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{9027973922382815624x^{3}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{2169209587527885604x^{3}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2825665471963221964x^{3}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{1917454163625x^{2}}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{1760222922207750x^{2}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{250831766414604375x^{2}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} + \frac{5804823046413491116x^{2}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{3678587392601496135x^{2}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{107614221404141882x^{2}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{7104122932882359335x^{2}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{11504724981750x}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{3520445844415500x}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{300998119697525250x}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} + \frac{7610811764598642616x}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{2452391595067664090x}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{1735675400194036628x}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{3988316125703763986x}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{17257087472625}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{2640334383311625}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{150499059848762625}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{4063474615916590875}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{735717478520299227}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{18261468225}{(-x^{2} - 6x - 8)^{\frac{15}{2}}} + \frac{5045604868475897061}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{2831076034833972813}{(-x^{2} - 6x - 8)^{\frac{29}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数arccos(x + 3) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{-213458046676875x^{14}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{8965237960428750x^{13}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{719432675836875x^{12}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{174822140228360625x^{12}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{25899576330127500x^{11}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2097865682740327500x^{11}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{949651132104675x^{10}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{427343009447103750x^{10}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{8084019845752926067x^{10}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{28489533963140250x^{9}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{4273430094471037500x^{9}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2387258890243677362x^{9}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{619337694850875x^{8}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{384608708502393375x^{8}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{8047835009739600107x^{8}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{6130978987669160225x^{8}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{14864104676421000x^{7}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{3076869668019147000x^{7}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{9114817528814797928x^{7}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{2696742994189445592x^{7}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{206445898283625x^{6}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{156073099102420500x^{6}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{2293178316609029866x^{6}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{4991626796567310484x^{6}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{9061950704748562985x^{6}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{3716026169105250x^{5}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{936438594614523000x^{5}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{2812604504433223452x^{5}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{8246381464494974888x^{5}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{322842664212425646x^{5}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{32596720781625x^{4}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{27870196268289375x^{4}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{3511644729804461250x^{4}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{2191860775771717178x^{4}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{2984778827781473701x^{4}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{8739108040536137339x^{4}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{391160649379500x^{3}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{111480785073157500x^{3}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{8427947351530707000x^{3}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} + \frac{9027973922382815624x^{3}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{2169209587527885604x^{3}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} - \frac{2825665471963221964x^{3}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{1917454163625x^{2}}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{1760222922207750x^{2}}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{250831766414604375x^{2}}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} + \frac{5804823046413491116x^{2}}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{3678587392601496135x^{2}}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{107614221404141882x^{2}}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{7104122932882359335x^{2}}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{11504724981750x}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{3520445844415500x}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{300998119697525250x}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} + \frac{7610811764598642616x}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{2452391595067664090x}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} + \frac{1735675400194036628x}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{3988316125703763986x}{(-x^{2} - 6x - 8)^{\frac{29}{2}}} - \frac{17257087472625}{(-x^{2} - 6x - 8)^{\frac{17}{2}}} - \frac{2640334383311625}{(-x^{2} - 6x - 8)^{\frac{19}{2}}} - \frac{150499059848762625}{(-x^{2} - 6x - 8)^{\frac{21}{2}}} - \frac{4063474615916590875}{(-x^{2} - 6x - 8)^{\frac{23}{2}}} - \frac{735717478520299227}{(-x^{2} - 6x - 8)^{\frac{25}{2}}} - \frac{18261468225}{(-x^{2} - 6x - 8)^{\frac{15}{2}}} + \frac{5045604868475897061}{(-x^{2} - 6x - 8)^{\frac{27}{2}}} + \frac{2831076034833972813}{(-x^{2} - 6x - 8)^{\frac{29}{2}}}\\ \end{split}\end{equation} \]
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