Đạo hàm của hàm số lượng giác (cực hay)

TiÕt 71:
TiÕt 71:
§¹o hµm cña hµm sè l­îng gi¸c (tiÕp)
§¹o hµm cña hµm sè l­îng gi¸c (tiÕp)
KiÓm tra bµi cò:
Nh¾c l¹i c¸c c«ng thøc tÝnh ®¹o hµm cña hµm l­îng gi¸c vµ giíi h¹n
sin x
x
¸p dông lµm bµi sau: tÝnh ®¹o hµm hs:
3 .siny x x=
(3 )'.sin 3 .(sin )'y x x x x
′
= +
3.sin 3 .cosx x x= +
Gi¶i.

Bµi míi
Bµi míi
Ho¹t ®éng I: TÝnh c¸c giíi h¹n d¹ng
sin x
x
Bµi 1: TÝnh c¸c giíi h¹n sau:
0
sin 4
a. lim
2
x
x
x
→ 0

2.sin 4
lim
2.2
x
x
x
→
=
0
sin 4
2.lim
4
x
x
x
→
=
2=
0
sin
b. lim
3

x
x
x
→
0
1
.sin

3
lim
1
.3
3
x
x
x
→
=
0
1 sin
.lim
3
x
x
x
→
=
1
3
=
2
2
0
sin 3
c.lim
x
x
x

→
2
2
0
9.sin 3
lim
9
x
x
x
→
=
2
2
0
sin 3
9.lim
(3 )
x
x
x
→
=
9=

Ho¹t ®éng II: §¹o hµm cña hµm th­êng gÆp
Bµi 2: TÝnh c¸c ®¹o hµm sau
a. (3a/SGK.169) cho hµm sè:
5sin 3cosy x x= −
(5sin ) (3cos )y x x

′ ′ ′
= −
5cos 3sinx x= +
b. (3b/SGK.169): tÝnh ®¹o hµm cña hµm sè:
sin cos
sin cos
x x
y
x x
+
=
−
( ) ( ) ( )
( )
2
sin cos .(sin cos ) sin cos . sin cos
sin cos
x x x x x x x x
y
x x
′ ′
+ − − − +
′
=
−
( ) ( ) ( )
( )
2
cos sin .(sin cos ) cos sin . sin cos
sin cos

x x x x x x x x
x x
− − − + +
=
−
( ) ( ) ( )
( )
2
sin cos .(sin cos ) cos sin . sin cos
sin cos
x x x x x x x x
x x
− − − − + +
=
−

( ) ( )
( )
2 2
2
sin cos cos sin
sin cos
x x x x
x x
− − − +
=
−
( )
2 2 2 2
2

sin 2sin .cos cos sin 2sin cos cos
sin cos
x x x x x x x x
x x
− + − − − −
=
−
( )
2 2
2
2sin 2cos
sin cos
x x
x x
− −
=
−
( )
2 2
2
2(sin cos )
sin cos
x x
x x
− +
=
−
( )
2
2

sin cosx x
−
=
−
c. TÝnh ®¹o hµm cña hµm sè sau:
2
1
( ).cot
2
y x x x= +
2 2
1 1
( ) .cot ( ).(cot )
2 2
y x x x x x x
′ ′ ′
= + + +
2
2
1 1 1
(2 ).cot ( ).
2 2 sin
x x x x
x
= + − +

Ho¹t ®éng nhãm
Ho¹t ®éng nhãm
Chia líp thµnh 4 nhãm , c¸c nhãm ho¹t ®éng trong 5p
Nhãm 1 vµ 3: TÝnh §H cña hs sau:

.coty x x=
Nhãm 2 vµ 4: TÝnh §H cña hs sau:
2
sin
2
x
y
x
=
+
§¸p ¸n
( ) .cot .(cot )y x x x x
′ ′ ′
= +
2
cos 1
1. .
sin sin
x
x
x x
= −
2
cos .sin
sin
x x x
x
−
=
§¸p ¸n

( ) ( )
( )
2 2
2
2
(sin ) . 2 2 .sin
2
x x x x
y
x
′
′
+ − +
′
=
+
( )
( )
2
2
2
cos . 2 2 .sin
2
x x x x
x
+ −
=
+