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

xx dx c

1

1.

1

ax b

ax b dx c

a

sin ' cosx x sin ' '.cosu u u sin cosxdx x c

1sin cosax b dx ax b c

a

cos ' sin x x cos ' '.sinu u u cos sinxdx x c

1cos sinax b dx ax b c

a

2

2

1tan ' 1 tan

cos

x x

x

2

2

'tan ' '. 1 tan

cos

u

u u u

u

2

1tan

cos

dx x c

x

2

1 1tan

cos

dx ax b c

ax b a

2

2

1cot ' 1 cot

sin

x x

x

2

2

'cot ' '. 1 cot

sin

uu u u

u

2

1cot

sin

dx x c

x

2

1 1cot

sin

dx ax b c

ax b a

1log '

lnax

x a

'log '

. lna

uu

u a

1lndx x c

x

1 1

lndx ax b c

ax b a

1ln ' x

x

'ln '

uu

u

' . lnx xa a a ' . ' . lnu ua a u a ln

x

xa

a dx c

a

. ln

x

xa

a dx c

a

'x xe 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 xC

a ax a 2 2

1

2

lndx x a

Ca x ax a 2 2

arcsindx x

Caa x

2 2

2 2

lndx

x x a Cx a

III. Vi phaân: ' .dy y dx

VD: 1

( ) ( )d ax b adx dx d ax ba

, (sin ) cosd x xdx , (cos ) sind x xdx ,

(ln )dx

d xx

, 2

(tan )cos

dxd x

x,

2(cot )

sin

dxd x

x . . .

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 ;

aa

a

.a a a

. .ab a b ;

a a

b b

0 0 1log ,M

ax M x a x a

1 0loga ; 1log

aa ;

log loga ab b

1

log log

aab b ;

logaa

log . log loga a abc b c

log log loga a a

bb c

c

log logb bc aa c ;

logaa

loglog log .log

logc

a a cc

bb c b

a

1log

logab

ba

0 1 a a a log log

a 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.

11 1. lim

x

xe

x

ex x

x

1

1lim.2

ax

a x

xln

1lim.3

0

a

x

xa

x

1lim.4

0

e

x

xa

a

xlog

1loglim.5

0