BAÛNG COÂNG THÖÙC ÑAÏO HAØM - NGUYEÂN HAØM
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
'
cos
x
x
sin
'
'. cos
u
u
u
sin
cos
xdx
x
c
1
sin
cos
ax
b dx
ax
b
c
a
cos
'
sin
x
x
cos
'
'.sin
u
u
u
cos
sin
xdx
x
c
1
cos
sin
ax
b dx
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
'
ln
a
x
x
a
'
log
'
. ln
a
u
u
u
a
1
ln
dx
x
c
x
1
1
ln
dx
ax
b
c
ax
b
a
1
ln
'
x
x
'
ln
'
u
u
u
'
. ln
x
x
a
a
a
'
.
' . ln
u
u
a
a u
a
ln
x
x
a
a dx
c
a
. ln
x
x
a
a
dx
c
a
'
x
x
e
e
'
' .
u
u
e
u e
x
x
e dx
e
c
1
ax
b
ax
b
e
dx
e
c
a
Boå sung:
2
2
1
arctan
dx
x
C
a
a
x
a
2
2
1
2
ln
dx
x
a
C
a
x
a
x
a
2
2
arcsin
dx
x
C
a
a
x
2
2
2
2
ln
dx
x
x
a
C
x
a
III. Vi phaân:
' .
dy
y dx
VD:
1
(
)
(
)
d ax
b
adx
dx
d ax
b
a
,
(sin )
cos
d
x
xdx
,
(cos
)
sin
d
x
xdx
,
(ln )
dx
d
x
x
,
2
(tan )
cos
dx
d
x
x
,
2
(cot
)
sin
dx
d
x
x
. . .
BAÛNG COÂNG THÖÙC MUÕõ - LOGARIT
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
0
0
1
log
,
M
a
x
M
x
a
x
a
1
0
log
a
;
1
log
a
a
;
log
log
a
a
b
b
1
log
log
a
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
;
log
a
a
log
log
log
. log
log
c
a
a
c
c
b
b
c
b
a
1
log
log
a
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
1
. lim
x
x
e
x
e
x
x
x
1
1
lim
.
2
a
x
a
x
x
ln
1
lim
.
3
0
a
x
x
a
x
1
lim
.
4
0
e
x
x
a
a
x
log
1
log
lim
.
5
0
