高等数学等价替换公式

导数公式

(1) (C)'=0

(2) (x μ)'=μ1x μ- (3) (sinX)'=cosX

(4) (cosX)'=-sinX (5) (tanA)'=2sec A

(6) (cotA)'=-2csc A (7) (secA)'=secAtanA

(8) (cscA)'=-cscAcotA (9) (x a )'=x a ln a

(10) (x e )'=x e (11) (㏒a x)'=1

ln x a

(12)(lnx)'=1x (13) (arcsinX)'

(14) (arccosX)'=-

(15) (arctanX)'=21

1X +

(16) (arccotX)'=-21

1X +

等价公式

1

01lim(1)1~n x x x n →+- 当0x →时,ln(1+x)~x 201cos 1lim 2x x

x →-= 当0x →时,1~x e x - 0sin lim 1x x

x →= 当0x →时,1~ln x a x a - 1lim(1)x x e x →∞+= 22221123...(1)(21)6n n n n ++++=++ 0tan lim 1x x

x →= 223333(1)123...4n n n +++++= 0arcsin lim 1x x

x →= 2200sin cos n n xdx xdx ππ=⎰⎰ 0ln(1)

lim 1x x x →+= 01

lim 1ln x x a x a →-=