考研数学常用微积分公式
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()/
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 +