高等数学常用公式汇总

1、高等数学常用公式汇总平方立方：a2b2(ab)(ab)a22abb2(ab)2a22abb2(ab)2a3b3 (ab)(a2abb2)(5)a3b3 (ab)(a2abb2)(6)a33a2b3ab2 b3(ab)3a33a2b3ab2 b3(ab)3一 222一-(8)abc2ab2bc2can nn 1 n 2.(9)a b (a b)(a a b倒数关系：111商的关系：平方关系：A2(x)A2(x)=1A2(x)+1A2(x)A2(x)+1A2(x)倍角公式：(2 oc 尸2 a , a(2 a )A2( a2( a 户2AZ(=1 % 2人2( a )(2 a )=2 a/仔2(

2、a)降幕公式：A2( a /2)=(1 a )/2A2( a /2)=(1 a )/2A2( a /2)=(1 a )/(1 a )(a /2) a /(1 a )=(1 a ) a两角和差：(aB)a,Ba,B(a+B)a , 3 a , (觉 B)a , 3 a , 3(a + 3 尸(a 3 )/(1 a , 3 ) (觉 B )=( a B )/(1 a B )积化和差:a3=(1/2)(a-f加)(aa3=(1/2)(a书加)(aa3=(1/2)(a-f加)(aa 3 (1/2)(“-+)( a和差化积：a 3 =2( a + 3 )/2阳)/2卜a 3 =2( a + 3 )/2阳

3、)/2卜a 3 =2( a + 3 )/2阳)/2卜 a B 2K a + B )/20()/2a特殊角的三角函数值:06432汽3-22支f()(0 )(30 )(45 )(60 )(90 )(180 )(270 )(360 )sin01/22/2V3/210-10cos1V3/2V2/21/20-101tan01 / 3173不存在0不存在0cot不存在Q11/上0不存在0不存在等价代换:4 / 4(1) sinx x1 2(5) 1 cosxx2基本求导公式：(1) (C)0, C是常学(3)(ax) axlna(5)(sin x) cosx 1(tan x) cos x(2)tanx-

4、 x(6) ln(1 x)x2sec x(3) arcsinx xx ,(7) e1x(2) (x )(log ax)(6) (cos x)(8)(cot x)(4) arctanx x(8) (1 x)a 1 ax1x1xln asin x122csc xsin x (sec x) (secx) tan x(10) (cscx) (csc x) cot x(11) (arcsin x)1Cx2(12) (arccosx)(13) (arctan x)11 x2(14) (arccot x)11 x2(15)(后12.x(10)dx2 cos x2sec xdx tanx Cdx2sin x2

5、,八csc xdx cotx C, 1、(16)(-)x基本积分公式:(1)0dx Ckdx kx C k为常数x 1(3) x dx C 1 1，八1八(4) dx ln | x | C x(11) secx tan xdx secx C(12) cscx cot xdx cscx C(13)dx2-arctan x C 或(1 xdx1 x2arc cot x C )(14)_dx_1 x2arcsin x C 或_dx_-1-x2arccosx C )高等数学常用公式汇总(15)(16)(17)(18)tan xdx ln |cosx | C ，cot xdx ln |sin x | C ，secxdx ln |secx tan x| C ，cscxdx ln | cscx