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 + − = + Ho¹t ®éng IV: §¹o hµm cña hµm hîp Bµi 3: TÝnh ®¹o hµm cña c¸c hs sau: a. (3f/SGK.169) tÝnh ®h cña hs: 2 sin 1y x= + ( ) 2 2 1 .cos 1y x x ′ ′ = + + ( ) 2 2 2 1 .cos 1 2. 1 x x x ′ + = + + 2 2 2 .cos 1 2. 1 x x x = + + 2 2 .cos 1 . 1 x x x = + + b. TÝnh ®h cña hµm sè sau: 2 cot(3 2 1)y x x= − + 2 2 2 (3 2 1) sin (3 2 1) x x y x x ′ − − + ′ = − + 2 2 6 2 sin (3 2 1) x x x − + = − + c. TÝnh ®h cña hµm sè sau: 2 2 tan (2 1)y x= + 2 2 2.tan(2 1).(tan(2 1))y x x ′ ′ = + + 2 2 2 2 (2 1) 2.tan(2 1). cos (2 1) x x x ′ + = + + 2 2 2 2 sin(2 1) 4 2. . cos(2 1) cos (2 1) x x x x + = + + 2 3 2 sin(2 1) 8 . cos (2 1) x x x + = + B©y giê Chóng ta cïng ch¬i trß ch¬i .