O HM DNG 1.TèM O HM BNG NH NGHA Phng phỏp : tỡm o hm theo nh ngha ta cú cỏch sau : Cỏch Bc Cho x mt s gia Lp t s x v tỡm s gia y = f ( x + x ) f ( x ) y x y x x lim Bc Tỡm gii hn f ( x ) f ( x0 ) f ' ( x0 ) = lim Cỏch p dng cụng thc x x0 x x0 Tỡm o hm ca cỏc hm s sau theo nh ngha ti cỏc im ó ch ra: y = f ( x ) = x3 x + y = f ( x ) = 2x2 x + x0 = x0 = a) ti b) ti DNG 2: TNH O HM BNG QUY TC V CễNG THC Cỏc quy tc : Cho u = u ( x) ; v = v ( x) ; C : l hng s ( u v ) ' = u ' v ' ( u.v ) ' = u '.v + v '.u ( C.u ) = C.u C u C u u '.v v '.u = = , v ( ) ữ ữ v v2 u u2 Nu y = f ( u ) , u = u ( x ) y x = yu u x Cỏc cụng thc : ( C) = ; ( x) = ( xn ) = n.xn1 ( ) = n.u n1.u , ( n Ơ , n 2) un ( x ) = 21x , ( x > 0) ( u ) = 2uu , ( u > 0) Bi 1: Tớnh o hm ca cỏc hm s: a) y = x3 x + x y= c) y= b) ( u v ) ' = u ' v ' x 3x + x + x x3 x + x y= d) 1 x + x 0,5 x 4 ( u.v ) ' = u '.v + v '.u Bi 2: Tớnh o hm ca cỏc hm s sau: y = (2 x 3)( x x) y = (x + 3x)(2 x) a) b) 2 y = ( x + 1)(5 x ) y = x(2 x 1)(3x + 2) c) d) Bi 3: Tớnh o hm ca cỏc hm s sau: a) y= 2x 4x b) y= x + 10 4x c) y= x + 5x 3x Bi 4: Tớnh o hm ca cỏc hm s sau: y = (1 x2 )3 y = ( x x )32 a) b) Bi 5: Tớnh o hm ca cỏc hm s sau: y = 2x 5x + a) u u '.v v '.u , ( v 0) ữ= v v2 d) ( u n ) = n.u n1.u ( u ) = 2uu 2x2 x + y= 2x + , ( n Ơ , n 2) , ( u > 0) y = ( x + 1) x + x + y = x 3x + b) c) f ( x ) = x3 Cõu 1: S gia ca hm s x0 = , ng vi v x =1 l: A 19 B -7 C D f ( x) = x x Cõu 2: S gia ca hm s theo x v l: x ( x + x ) x ( x + x ) 2x + x 2x A B C D y f ( x) = 2x x x Cõu 3: T s ca hm s theo x v l: 2x x x A B C D Cõu :o hm ca hm s l: A B C D Cõu 5: o hm ca hm s l: A B C D x) x + 1) Cõu 6.Tớnh o hm y = (2x (x / y = x 15 x + 10 x + y / = x + 15 x + 10 x A B / y = x 15 x + 10 x y / = x3 15 x 10 x C D y = ( x + x )(5 x ) Cõu 7.Tớnh o hm y ' = 12 x + x + 10 x + y ' = 12 x x 10 x + A B y ' = 12 x + x + 10 x y ' = 12 x x + 10 x + C D y= x 1 + 2x Cõu Tớnh o hm ca hm s sau: y/ = y/ = y/ = 2 ( 1+ 2x) ( + 2x) ( + 2x) A B C y' = (1 + x )2 D y = ( x 2) x + Cõu 9.Tớnh o hm x2 2x + 2x2 2x + 2x 2x + 2x2 x + y' = y' = y' = y' = x2 + x2 + x2 +1 x2 + A B C D y = x x2 + Cõu 10.Tớnh o hm y' = A 2x2 + x2 + y' = B 2x2 + x2 + y' = C 2x2 + x2 + y' = D 2x2 + x2 + Dng PHNG TRèNH- BT PHNG TRèNH CHA O HM Bi Cho vi y= Bi Cho x3 x2 y = + 2x Gii bt phng trỡnh x x + 10 x + 3 y ' Gii bt phng trỡnh y, y = x3 4x + 6x Bi Cho hm s Gii bt phng trỡnh y>1 f ( x) = x + x , g ( x) = 3x + x + Bi 4.Cho Gii bt phng trỡnh: f ( x) = x x + , g ( x) = x + Bi 5.Cho y= Bi Cho x +3 x +1 x f ' ( x ) > g ' ( x) Gii bt phng trỡnh: y ' Gii bt phng trỡnh: f '( x) Bi 7.Gii bt phng trỡnh : vi x2 x + f ( x) = x x +x+2 x y= Bi 8.Gii bt phng trỡnh :y/< , f ( x) = x3 x + x Cõu Cho hm s x A hay x Cõu2 Cho hm s A x B f ' ( x) Gii bt phng trỡnh B x C x 1 f ( x) = x x + x 3 x Cõu 3.Cho haứm soỏ hay x D x Gii bt phng trỡnh: x hay x C D 1 f ( x) = x3 + x x + x hay x B x C x D f ' ( x) x Giaỷi baỏt phửụng trỡnh x hay x x x x A B C D y = x 6x + 9x + y' Cõu 4.Cho hm s Gii bt phng trỡnh A f ' ( x ) > g ' ( x) f '( x ) x x3 3x + 5x f ( x) = Cõu 5.Cho hm s x A B x5 C Cõu 6.Cho hm s < x < A D B Gii bt phng trỡnh: C < x < x2 + C D A y = x 3x + Cõu 9.Cho A B C C x 0x2 , D x hay x C v hm s x D g ( x) = x2 cú th (C) f ( x) g ( x) 17 + 17 x hay x 4 17 + 17 x hay x> 4 Cõu 11.Cho hm s x Gii bt phng trỡnh y f ( x ) = x 3x + Gii bt phng trỡnh : A 2 x hay x Cõu 10.Cho hm s , bit f ( x) = x x + x x hay x B < x f '( x ) < Gii bt phng trỡnh: B < x < 1+ x D 2x 1 1+ hay x > 2 g ( x) = x3 x < hay x> Cõu 7.Cho hm s A x y = x + x + x f (x) = x< Tỡm x f/(x)0 B D 17 x2 17 + 17 x 4 y = f ( x ) = x x + x + 2013 f ( x ) > Gii bt phng trỡnh: A < x D < x g ' ( x) Gii bt phng trỡnh: y ' Gii bt phng trỡnh: f '( x) Bi 7.Gii bt phng trỡnh :... 8.Gii bt phng trỡnh :y/< , f ( x) = x3 x + x Cõu Cho hm s x A hay x Cõu2 Cho hm s A x B f ' ( x) Gii bt phng trỡnh B x C x 1 f ( x) = x x + x 3 x Cõu 3.Cho haứm soỏ hay x D x Gii bt