Bài tập: Đạo hàm hàm số lượng giác

a. Ph¸t biÓu c«ng thøc ®¹o hµm cña c¸c hµm sè l­îng gi¸c.
(sinx)’ = cosx
Rx∈∀
(cosx)’ = sinx
Rx∈∀
'
2
1
( ) ( ; ),( )
cos 2 2
tanx x k k k Z
x
π π
π π
= ∀ ∈ − + + ∈
'
2
1
(cot ) ( ;( 1) ),( )
sin
x x k k k Z
x
π π
= − ∀ ∈ + ∈
b. C«ng thøc ®¹o hµm cña hµm hîp.
(sinu)’ =u’ cosu (cosu)’ =- u’sinu
'
'
2
(tan )
cos

u
u
u
=
'
'
2
(cot )
sin
u
u
u
= −
KiÓm tra bµi cò
c. Giíi h¹n
0
sin
lim 1
x
x
x
→
=
0
sin ( )
lim 1
( )
x x
f x
f x

→
=
0
0
( ) 0
lim ( ) 0
x x
f x x x
f x
→
≠ ∀ ≠



=


Víi
TiÕt 82: LuyÖn TËp
Bµi 28: T×m c¸c giíi h¹n sau
0
tan 2
)lim
sin 5
x
x
a
x
→
2

0
1 cos
)lim
sin 2
x
x
b
x x
→
−
Gi¶i
0 0
0
sin 2
2
tan 2 sin 2
2
)lim lim lim
sin 5
sin5 cos2 .sin5
5 .
5
x x
x
x
x
x x
x
a
x

x x x
x
x
→ →
→
= =
2
5
=
V×
0
lim cos2 1
x
x
→
=
2
2 2
0 0
0
sin
( )
1 cos sin
)lim lim lim
sin 2
sin 2 sin 2
2
2
x x
x

x
x x
x
b
x
x x x x
x
→ →
→
−
= =
1
2
=
Bµi 29: T×m c¸c giíi h¹n sau
a) y = sin(x
2
-3x+2)
d) y = tan(sinx)
) cos 2 1c y x= +
Gi¶i
2
) ' (2 3)cos( 3 3 )a y x x x x= − − +
1
) ' ( 2 1)sin 2 1 sin 2 1
2 1
c y x x x
x
= − + + = − +
+

2 2 2
(sin )' cos 2
) '
cos (sin ) cos (sin ) sin 2
x x
d y
x x x
= = = −