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 ' cosx x sin ' '.cosu u u sin cosxdx x c
1
sin cosax b dx ax b c
a
cos ' sin x x cos ' '.sinu u u cos sinxdx x c
1
cos sinax 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 '
lna
x
x a
'
log '
.lna
u
u
u a 1
lndx x c
x
1 1
lndx ax b c
ax b a
1
ln 'x
x
'
ln '
u
u
u
' .lnx x
a a a ' . '.lnu 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
1ax b ax b
e dx e c
a
Boå sung:
2 2
1
arctan
dx x
C
a ax a 2 2
1
2
ln
dx x a
C
a x ax a 2 2
arcsin
dx x
C
aa 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 ) cosd x xdx , (cos ) sind x xdx ,
(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
. .ab a b ;
a a
b b
0 0 1log ,M
a
x M x a x a
1 0loga ; 1loga
a ;
log loga a
b b
1
log logaa
b b ;
loga
a
log . log loga a a
bc b c
log log loga a a
b
b c
c
log logb b
c a
a c ;
loga
a
log
log log .log
log
c
a a c
c
b
b c b
a
1
log
loga
b
b
a
0 1
a a a log loga a
1
:a a a
0 1
:a a a
1 : log loga a
a
0 1 : log loga a
a
II.Moät soá giôùi haïn thöôøng gaëp.
1
1 1. lim
x
x
e
x
ex x
x
1
1lim.2
a
x
ax
x
ln
1
lim.3 0
a
x
x
a
x
1
lim.4 0
e
x
x
a
a
x
log
1log
lim.5 0
