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File0025 - 108 Chapter 3 Differentiation 3.2...

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Unformatted text preview: 108 Chapter 3 Differentiation 3.2 DIFFERENTIATION RULES FOR POLYNOMIALS, EXPONENTIALS, PRODUCTS, AND QUOTIENTS 1. y:_x2+3 : %¥:%(—x2)+§;(3)=—2x+0:—2m 2 §i§=—2 2. y=x2+x+8 : §§=2x+1+0=2x+1=> 31—2122 3. s = 5t3 — 3:5 2 % = $56) — g (3t5) = 15t2 —15t4 => ‘31—? : g; (15:2) — % (15:4) = 30: — 60t3 4. w : 327 -— 723 + 2122 => d—w : 2126 —2122 +422 => dzw ~126z5 — 422+42 dz d?— 5, y %—x+2ex :> §§=4xZ—1+2ex 2 :j—fggzsx+2ex 6. yz§+§+§ : §§2x2+x+§ => §f3é=2x+1+0=2><+1 7- W=3Z‘2—Z‘1 ;> ‘i-‘Z=-6Z‘3+Z‘2=;—f+;% => %=ISz—4—2z-3=1§-% 8. s=—2r1+4r2 => fizZt'Z—St’3zé—g => %=—4t_3+24t‘4=—:§+2K—44 9. y=6x2—10x—5x”2 => g§=12x—10+10x~3 =12x—10+i—2=> géézlz~0—30x-4=12—§79 _ _ _ —3 gx___ —4__ 3 fl_ _ —5_-1 10.y——4 2x x :> dx— 2+3X ~ 2+3: dx2~0 12x — x5 _172 5—1 dr__g —3 §~2_—_2 _5_ g3;_ —4_ —3_;_; 11.r—§s —§s :E— 35 +23 —353+2s2=>d52—25 SS ‘54 $3 12. r : 129‘1 — 46-3 + 6-4 :> 51—; = —126‘2 +126-4 40-5 = 3,122 + g 55 => 3;; — 240-3 — 480-5 + 200*6 =%—%+% 13. (a) y=(3—x2)(x3—x+l) => y’:(34x2)-§—x(x3—x+1)+(x3—x+1)-ad;(3—x2) =(3—x?)(3x2—1)+(x3—x+1)(—2x)=—5x4+12x2—2x—3 (b) y=~x5+4x3—x2—3X+3 => y’=—5X4+12x2—2x—3 14. (a) y=(x—1)(x2+x+1) :> y’=(x~~1)(2x+1)+(x2+x+1)(1)=3x2 (b) y=(x—1)(x2+x+1)=x3—1 => y’=3x2 15. (a) y‘(x2 : 1)(x : 5+3 —> y’—(x2+1)-dix(x+5+§)+(x+5+§)-§;(x2+1) =(x2+1)(1—x‘2)+(x+5+x_1)(2x):(x2—1+1—x_2)+(2x2+10x+2)=3x2+10x+2—;17 (b) y:x3+5x2+2x+5+§ => y’:3x2+10x+2—x1—2 16. y:(x+%) (x—l+1) X (a) y’:(x+x-1)-(1+x-2)+(x—x-l+1)(1ax-2)=2x+1—i;+;% X (b) y=x2+x+%—;17 :> y’=2x+1—;17+;25 / I 17.y=gifg;usethequotientrulezu—2x15z1ndv 3x 2 > u’ 23nd v’=3 => y'= Egg—fl ._ (3x‘2)(2)—(2X+5)(3) _ 6x—4—6x—15 _ —19 - (3x ~ 2)2 _ (3x 7 2)i _ (3x 7 2)2 ...
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