{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 3 30

# Chapter 3 30 - 180 CHAPTER 3 DIFFERENTIATION RULES_14...

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: 180 CHAPTER 3 DIFFERENTIATION RULES _14 26.G(y):(%:%)5 => my) 2 Mtg—11W [(342 + 2y) I 2 2012 + 2304(1/ —1)3I2(y2 + 2y) — 5(y —1)(y +1)] (112+2y)10 #204 y-1)3 [(2312 +4y)+ +(~5y2+5)l 2(y—1)3(‘3y2+4y+5) (1/2 + 2106 (y2 + 2y)6 27. =—L :» y m r2 «mt/r2142 _ 2 _ _______ ylgﬁmm—r-étrul) 1/2(2r)”+ m_ r2+1 (r2+1)2 ( r2+1) (r2+1)2 2 1 _ 2 :_——(r + I T :—————-1 or(7"2+1)_3/2 ( 7‘2+1)3 (7“2+1)3/2 Another solution: Write y as a product and make use of the Product Rule. y : r(r2 + 1) _1/2 :> y’ =T-—%(T2+ 1) 3/2(2r)+ (r2+1)‘1/2-1 : (7‘2 + 1)’3/2[—r2 + (r2 + 1f] : (r2 + 1Y3” (1) : (r2 + 1)‘3/2 The step that students usually have trouble with is factoring out (r2 + 1) 73/2. But this is no different than factoring out m2 from \$2 + :35; that is. we are just factoring out a factor with the smallest exponent that appears on it. In this case. —% is smaller than 7%. 2” e 28. = —— => y Cu +6—u / (eu + 6*”) (6274 . 2) # e2u(eu _ e—u) 6211 (26” + 26—” _ eu + 6711.) — €2u(eu + 36—”) y - (en ‘I' 67102 (6“ + 6—“)2 i (6" + e‘“)2 Another solution: Eliminate negative exponents by ﬁrst changing the form of y. 271. u 3n 6 e g e :> y : —— ~ — _ eu +eﬁu an 621; + 1 / (62“ + 1) (363u) _ e3u (26271.) e3u (362“ + 3 _ 262a) eBu (€2u + 3) (621; + 1)2 (6211. + 1)2 (6211. + 1)2 29. y : tan(cos 1:) :> y’ : sec2(cos w) - (i sin w) : # sina:sec2 (cos m) 30‘ y : sin2 1; cos ac , cosac (2 sin :1: cos 1:) ; sin2 ac (~ sin :13) _ sinm (2 cos2 a: + sin2 ac) _ sinm (1 + cos2 3:) y — cos2 a: cos2 30 cos2 ac : sings (1 + sec2 :13) . . 2 . . Another method: 3; : tan w smx => y' : sec2 1: sum: + tan 1: cos w : sec 3: sm m + \$111 w 31. Using Formula 5 and the Chain Rule, y : 25"“ 7“ => y' : 25in "1 (1n 2) - ;ld— (sin 7m) : 251“ "9” (ln 2) - cos 7m: - 7r : 2Sin 7”” (7r 1n 2) cos 7m 3: 32. y : tan2(36) : (tan 36)2 :> y' : 2(tan 36) , % (tan 30) : Ztan 30 ~ sec2 36 - 3 : (Stan 36 sec2 39 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online