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C¸c c«ng thøc hµm sè mò – logarit cÇn nhí I - c«ng thøc cña hµm sè mò

1. a m .a n = a m + n

)n

4.(a.b = a n.b n

a a 5.  = b  b

6. a.b = a . b

n

n

n

n

m

n

)

m

=a

m

n

9.

n

m

n

a =

; m < n : khi 0 < a < 1

n

n

n

8. a = ( a

n

n

m

n 3. a m  = a m.n

n

a a = b b 10.a > a ⇔ m > n : khi a > 1 11.a < b, a, b : le  → a < b 7.

m m− n a 2. n = a a

n

II- C«ng thøc hµm sè logarit

1.α = log b ⇔ a = b DK:b> 0, 0 < a ≠ 1 α

a

2. log 1 = 0 ; log a = 1 a

a

3. log a = b ; a b

loga b

a

4. log ( b.c ) = log b + log c

=b

a

b 5. log   = log b − log c c 1 7. log b = log b α a

a

aα

a

6. log b = a

a

log b lg b ln b = = log a lg a ln a c

c

1 8. log b = log a a

a

b

9. log b > log c ⇔ b > c : khi : a > 1; b < c: khi: 0 < a < 1 a

a

a

III- §¹o hµm cña hµm sè : 1. y = a  → y ' = a ln a x

2. y = e  → y ' = e

x

3. y = log x  → y ' = a

x

1 x ln a

4. y = ln x  → y ' =

IV- Giíi h¹n cña hµm sè:

x

1 x

2. lim( 1 + x ) = e

x

1  1. lim 1 +  = e x 

1 x

x →∞

a −1 = ln a x

x→ ∞

x

3. lim x →0

4. lim x →0

(1 + x ) x

a

=a

5. lim x →0

log (1 + x ) = log e x a

a

n

m.n

a