考研数学常用微积分公式背诵表

()/

x μ=1x μμ-

()/

x a =ln x a a

()

/

x e =x e

()/

log a x =

1

ln x a

()

/

ln x =

1x

()

/

sin x =cos x

()/

cos x =sin x - ()/

tan x =2sec x ()/

cot x =2

csc x - ()/

sec x =sec tan x x ()

/

csc x =csc cot x x -

()

/

arcsin x

=

()

/

arccos x

=()

/

arctan x =

2

1

1x

+ ()/

arccot x =2

11x -

+ ()

/

uv =//u v uv +

/

u v ??= ???

//

2

u v uv

v - kdx =?kx

x dx μ

=?1

1x μμ++

dx

x =?ln x 21dx

x =+?arctan x

=arcsin x

cos xdx =?sin x

sin xdx =?cos x -

2sec xdx =?tan x 2c cs xdx =?cot x -

sec tan x xdx =?sec x csc cot x xdx =?csc x - x

e dx =?x

e

x a dx =?ln x

a a

tan xdx =?ln cos x - cot xdx =?ln sin x sec xdx =?ln sec tan x x + csc xdx =?ln csc cot x x -

22

1dx x a =+?1arctan x

a a 22

1dx x a =-?1ln 2x a a x a

-+

=

ln x

=arcsin x

a

等价无穷小()0x →

sin ~x x tan ~x x

arcsin ~x x arctan ~x x

ln(1)~x +x 1~x e -x 1cos ~

x -212x

1~1

2

x

1~x a -ln x a

渐近线k =()

lim

x f x x

→∞

b =()lim x f x kx →∞-???

? 曲率k =

()

//

3

/22

1y y +