{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 3 44

# Chapter 3 44 - 194 CHAPTER 3 DIFFERENTIATION RULES 40...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 194 CHAPTER 3 DIFFERENTIATION RULES 40- 31" = mp => qy‘1—1y' =pnc"’"1 => y = = : __ : _\$(p/q)v1 (Mg—1 qu qu q _ 1 d 1 41.y=tan1\/:-i ﬁ y’=——-——-—.—-— x : (1“1/2) 1 1+(ﬁ)2 dm(‘/_) 1+1: 23” 2ﬁ(1+a:) 42. y = vtarflcc =(tatn’1a:)1/2 :> _ _ d _ 1 1 1 I _ 1 1 1/2 1 y —2(tan :3) -—(tan x):————- :_.__.—__ d3: 2vtan_1:!: 1+9; 2m(1+m2) 43. y : sin—1(2w + 1) => 1 d y’=_————.—(2g;+1):____1_—.2:__2—_:_1_ 1 — (2m—I— 1)2 dl‘ V1 — (4m2 +4zc+ 1) \/~4:c2 —4x V-m'e’ — m 44. h(x) = \/1 — x2 arcsinrn => 1 . h/(x =1/1—m2 . __ +arcsinx[l 1_\$2 ~1/2 _2 ]: 1e marcsmzc ) ,/1_\$2 2( ) ( w) ”m 45. H(:L') = (1 + 932) arctanm :> H'(w) = (1 + 112) + (arctan\$)(2a:) = 1 + 2.2: arctanm 1+2:2 46. y=tan_1(:c—\/w2+1) => y' _ 1 (1 m ) 1 (VﬂI—l—m) 1+(\$_ /——\$2+1)2 w2+1 1+\$2e2x\/m2+1+\$2+1 x/m2—I—1 : \/:c2+1—a: _ x/ar2-I—1—a: 2(1+m2—x\/w2+1)\/932+1 2[\/x2+1(1+x2)—x(m2+1)] \/\$2+1«x 1 — 2[(1 ”Mm — x)] 2(1 + x2) 47. h(t) : cot—1(t) + cot’1(1/t) ﬁ , 1 1 d1 1 t2 1 1 1 hm- 2 2‘ — 2 2 ~ —2 —— 2+2 :0 1+t 1+(1/t) dtt 1+t t +1 t 1+t t +1 Note that this makes sense because h(t) : g fort > 0 and h(t) : —% fort < 0. _ *1 _ _ 2 I_ —1 ___.’E—_ _____ 48.y_avcos cc V1 :1: => yﬁcos a: ﬂ+ﬂ§—COS a: 1 d 28\$ 49. 2 cos-1 e2I _> ’ _ . e27” ! _.____ y ( ) y 1 _ (6”? dm ( ) J1 _ 641 1 sin0 . z ' : .————— _ ' 6 : ___—._ 50 y arctan(cos 0) => 3,] 1 + (cos m2 ( Sln ) 1 + cos2 0 51. f(m) : ex ! m2 arctanw :> 10 f'(:v) : e1 — [302(1 +132) + (arctan \$)(2w)] 3’2 L1 : ea” 7 1 +232 7 2marctanm _2 A 3 This is reasonable because the graphs show that f is increasing when f ' is positive. and f’ is zero when f has a minimum. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online