Bài giảng Giải tích 11 chương 5 bài 3 Đạo hàm của hàm số lượng giác

BI 3:





 
x∆
Nhc li cc quy tc tnh đo hm ca hm s y = f(x)
ti đim x ty  b!ng đ#nh ngh$a ?
 
    y f x x f x∆ = + ∆ − =

 
x
y y
x x
∆ →
∆ ∆
⇒ =
∆ ∆
Dng đ#nh ngh$a h'y
tnh đo hm ca
hm s y = sinx



Dng đ#nh ngh$a h'y tnh đo hm ca hm
s y = sinx




 !
"#$%
Ta c:


 !
"#$%
Ta c:

x∆
   y f x x f x∆ = + ∆ −
&  &x x x= + ∆ −
' (
'
x x x
c
+ ∆ +
 
=
 ÷
 
&
'
x x x+ ∆ −
 
 ÷
 
' ( &
' '

x x
c x
∆ ∆
 
= +
 ÷
 
' ( &
' '
x x
c x
y
x x
∆ ∆
 
+
 ÷
∆
 
=
∆ ∆
&
'
' ( 
'
x
x
c x
x
∆

∆
 
= +
 ÷
∆
 


x
y
x
∆ →
∆
∆

&
'
 ' ( 
'
x
x
x
c x
x
∆ →
∆
 
 
∆
 

= +
 
 ÷
∆
 
 
 

 ( ( )
'
x
x
c x x
∆ →
∆
 
+ =
 ÷
 

&
'
 ' 
x
x
x
∆ →
∆
 
 ÷

=
 ÷
∆
 ÷
 
Tnh gii
hn ny
như th
no ?

*&+
+,&+#&-&+.
/-&+*0
1234&
5++6
78888889:::≈
& x
x
& 70
70
& 70
70
& 70
70
788889::::;≈
7888888889:≈

&
 0
x

x
x
→
=

&  
 0
 
x
u x
u x
→
=
x →
  u x →
V d 1: *&+
Gii:
!
V d 2 *&+
Gii:
!

&

x
x
x
→
 
& & 0

  
(
x x
x x
x x x
→ →
 
=
 ÷
 
 
& 0
  00 0
(
x x
x
x x
→ →
= = =

& '

x
x
x
→
 
& ' & '
  '
'

x x
x x
x x
→ →
 
=
 ÷
 

& '
' '0 '
'
x
x
x
→
= = =

& x
x
Dng đ#nh ngh$a h'y tnh đo hm ca hm
s y = sinx



 !
"#$%
V:
Vy


 !
"#$%
V:
Vy
x∆
   y f x x f x∆ = + ∆ −
&  &x x x= + ∆ −
' (
'
x x x
c
+ ∆ +
 
=
 ÷
 
&
'
x x x+ ∆ −
 
 ÷
 
' ( &
' '
x x
c x
∆ ∆
 
= +
 ÷

 
' ( &
' '
x x
c x
y
x x
∆ ∆
 
+
 ÷
∆
 
=
∆ ∆
&
'
' ( 
'
x
x
c x
x
∆
∆
 
= +
 ÷
∆
 



x
y
x
∆ →
∆
∆

&
'
 ' ( 
'
x
x
x
c x
x
∆ →
∆
 
 
∆
 
= +
 
 ÷
∆
 
 

 
 
&
'
 (   '
'
x x
x
x
c x
x
∆ → ∆ →
∆
 
 ÷
∆
 
= +
 ÷
 ÷
∆
 
 ÷
 

 ( ( )
'
x
x
c x x

∆ →
∆
 
+ =
 ÷
 
  
& & &
' ' '
 '  '  0
'
' '
x x x
x x x
x x
x
∆ → ∆ → ∆ →
∆ ∆ ∆
   
 ÷  ÷
= = =
 ÷  ÷
∆ ∆
∆
 ÷  ÷
   

 ( 0 (
x
y

x x
x
∆ →
∆
⇒ = =
∆
< & < (y x x= =
2. Đo hm ca hm sô
/-&+*'
=>?&!(+@A
BC>?&A?+6
&y x=
x R∈
& < (x x=& < (x x=
& < <(u u u=
2. Đo hm ca hm sô
V d 3 6(++

/D+6>?&
!
&y x=
& :
E
y x
π
 
= +
 ÷
 
:

E
u x
π
= +
<
<
:
(
x
u
u
y u

=

=

< < <

x u x
y y u=
:( :
E
x
π
 
= +
 ÷
 
14A*FG

0H *&+
'H 6(++
H
H

:
&
'

x
x
x
→
( )
'
'& :y x=
&y x=
I*FGAJ+&
0H *&+


& x
x

:
&
'

x
x

x
→
 
: :
& &
' '
 
' :

: '
x x
x x
x
x
→ →
=

:
&
: : :
'
 0
:
' ' '
'
x
x
x
→
= = =

I*FGAJ(++>?&
'H 6(++
H

H


( )
'
'& :y x=
( ) ( ) ( )
<
<
' ' '
< ' & : ' : ( :y x x x
 
= =
 
( )
'
0' ( :x x=
&y x=
( ) ( )
< <
< & (y x x x= =
0
(
'
x
x

=
5++6
I?+6
+&+

&
 0
x
x
x
→
=

&  
 0
 
x
u x
u x
→
=
& < (x x=
& < <(u u u=
x →
  u x →