高等数学必备公式 1、幂函数(4个): (1)anmaamnnmnammn (2)na a1 am (3)ama (4)am2、对数函数(4个): (1)lnablnalnb (2)lnalnalnb b (3)lnablna (4)NlneNelnN b3、三角函数(10个): (1)sin2xcos2x1 (2)sin2x2sinxcosx (3)cos2xcosxsinx2cosx112sinx (4)sin2x1cos2x (5)cos2x1cos2x222222 2 (6)1tanxsecx (7) 1cotxcscx 22211 (9)cosx cscxsecx1 (10)tanx cotx (8)sinx4、等价无穷小(11个): 当0时: sin~ arcsin~ tan~ arctan~2nx3x3x3当x0时: tanxsinx~ tanxx~ xsinx~236 e1~ ln(1)~ 1cos~2 n11~5、求导公式(18个) 幂函数: (1)(c)=0 (2)(x)x(3)11 (4) x2x第 1 页 共 3 页 1 x21x 指数对数: (5)(ax)axlna (6)(ex)ex (7)(logax)11 (8)(lnx) xlnax三角函数: (9)(sinx)cosx (10)(cosx)sinx (11)(tanx)sec2x (12)(cotx)csc2x (13)(secx)secxtanx (14)(cscx)cscxcotx 反三角函数:(15)(arcsinx) (17)(arctanx)11x2 (16)(arccosx)11x2 11 (18)(arccotx)1x2 1x26、积分公式(24个) 幂函数: (1)kdxkxC (3)1 (2)xdxxC(1) 111dxC (4)x2x1dx2xC x (5)1xdxlnxC xxa指数函数:(6)adxC1) (7)exdxexC lna 三角函数:(8) sinxdxcosxC (9) cosxdxsinxC (10)tanxdxlncosxC(11) cotxdxlnsinxC (12) (14)secxtanxdxsecxC (13)cscxcotxdxcscxC dx12cos2xsecxdxtanxC (15)sin2xdxcsc2xdxcotxC (16)secxdxlnsecxtanxC (17)cscxdxlncscxcotxC (18)11x2dxarcsinxC (19)1a2x2dxarcsinxC a (20)11x1 (21)dxarctanC dxarctanxCa2x2a1x2a (22)1x2a21x2a2dxlnxx2a2C (23)dxlnxx2a2C 第 2 页 共 3 页 本文来源:https://www.wddqw.com/doc/917529354228915f804d2b160b4e767f5bcf8016.html