1. BAÛNG COÂNG THÖÙC ÑAÏO HAØM - NGUYEÂN HAØM
Traàn Quang - 01674718379
I. Caùc coâng thöùc tính ñaïo haøm.
1. (u v)' u ' v ' 2.(u.v)' u '.v u.v ' 3.
'
2
u u '.v u.v '
v v
Heä Quaû: 1. ku ' k.u ' 2.
'
2
1 v '
v v
II. Ñaïo haøm vaø nguyeân haøm caùc haøm soá sô caáp.
Bảng đạo hàm
Bảng nguyên hàm
  1 x ' x   1  ' . ' .    u  u u  
1
, 1
1
x
x dx c

 


   
   
 
1
1
.
1
ax b
ax b dx c
a





  
 
sin x'  cos x sinu'  u'.cosu  sin xdx  cos x  c
   
1
sin ax b dx cos ax b c
a
     
cos x'  sin x cosu'  u'.sinu  cos xdx  sin x  c
   
1
cos ax b dx sin ax b c
a
    
  2
2
1
tan ' 1 tan
cos
x    x
x
    2
2
'
tan ' ' . 1 tan
cos
  
u
u u u
u
2
1
tan
cos
dx x c
x
  
 
  2
1 1
tan
cos
dx ax b c
ax b a
  
 
    2
2
1
cot ' 1 cot
sin

x     x
x
    2
2
'
cot ' ' . 1 cot
sin

   
u
u u u
u
2
1
cot
sin
dx x c
x
     
  2
1 1
cot
sin
dx ax b c
ax b a
   
 
1
log '
a ln x
x a
'
log '
a .ln
u
u
u a
1
dx ln x c
x
  
1 1
dx ln ax b c
ax b a
  
 
1
lnx '
x
'
ln '
u
u
u
ax ' ax . lna au ' au .u '.lna ln
x
x
a
a dx c
a
  
.ln
 
 


   
x
x
a
a dx c
a
ex ' ex  ' '. u u e  u e x x  e dx  e  c
1
ax b ax b e dx e c
a
    
III. Vi phaân: dy y ' .dx
VD:
1
d(ax b) adx dx d(ax b)
a
, d(sinx) cosxdx , d(cosx) sinxdx ,
(ln )
dx
d x
x
,
2 (tan )
cos
dx
d x
x
,
2 (cot )
sin
dx
d x
x
. . .

2. BAÛNG COÂNG THÖÙC MUÕõ - LOGARIT
Traàn Quang - 01674718379
I. Coâng thöùc haøm soá Muõ vaø Logarit.
Haùm soá muõ Haøm soá Logarit
1


a
a
;

a  a
a .a a  ;

 

a
a
a
 
a . a a

a.b a .b ;



a a
b b
log M 0 , 0 1
a x M x a x a
log 1 0 a
; log 1 a a ;  log  log a a b b
1
 
log loga a
b b;  log  a a
log . log log a a a b c b c
log log log a a a
b
b c
c
log log b b c a a c ;  
loga a
log
log log .log
log
c
a a c
c
b
b c b
a
1
log
a log
b
b
a
  0 1 a a   a log  log    a a
1   a : a a  
0 1   a : a a  
1 : log  log    a a a
0 1 : log  log    a a a
II.Moät soá giôùi haïn thöôøng gaëp.
1
1. lim 1
x
x
e
x
 xx e
x
 

1
2.lim 1
a
x
ax
x
ln
1
3.lim
0



 
a
x
x a
x



1
4.lim
0
 
e
x
x
a
a
x
log
log 1
5.lim
0


