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ma1012_hw14_201012

Y dx 4 1 c sin 3 t cos 2 acos a bb 2 c2 sin a

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Unformatted text preview: tc 3 22.x dx xy "Î#t œ 1 Ê 3x c y c x dx c 3y " † d c 0 c " dy t)c c œ# c dy x c' & 19. ˆx cÈcb y œ (3wc t)"Î#ˆ Ê ‰dp c " b$Î# ˆc"Î#œ dt #Ê a3y"Î# xb dx œ y "Î# 3x 2 Ê" dx œ " dt # œ ax x cos xb b asincœxb ap #œ" ‰ bcc a aÊcos# xb (†csin" x)b #œ a#1(3$cbt)#3dx b ax(3b 1t)cœ c " (3 c # b 1bc$Î# È3 c#t b x#3y c x œ c b 1 3 3 3 y œ x c ax b cos x a x‰ 10. y x x x b b b † acx b "b # dy 2 È È 3dr y œ $ 2x œ (2x)"Î$ Ê dy œ " (2x)c#Î$ † 2 œ 3x b . 4. y )œ %) b5x œ (5x)"Î% Ê dx œ (cot csc )) dx 3 ) cotdr )c" Ê È œ c(csc ) ‰ ˆcot")‰c# dd) (cscathematics csc ) cotb cotcsc ) œ csc4. ) berivatives Part II ) ) " ‰ ) b cot )) œ È ) " )) # "b d) )‹ ˆ sec (csc‹ Š c ) b tan ˆM Šsec È) tan I: Homework 1(csc D cot )) ) È‹ d) œ Šsec ) ) œ sin a) b (csin 2x ) d) Ê)) bœ (2)) acos a) bb † d) a) b (2 cos x 1. y œ ) dx 4 1 c sin 3) t ‰ (cos 2)# acos a)# bb (2)) œ c2 sin a)# b sin (#)) b 2) cos (2)) cos a)# b # 2. y œ x Ê dx œc5x " 4 (5x)c$Î% † 5 œ 5 4x ) 161 149 ax b 1 b d d # # # # " " 35. cos# x sin Ê dr x cos d x sinc& œ (2r #œ sin a)# bxcos (2))t)$ d (1 œ sin a) b (csin 2)) (2)) b cos (2)) acos a) bb † d) a) b sec 1t)x† c (sec 1t) x b xsec 1t)(secœ ctancos: †xdt d) t) œ 21 sec# 1t tan 1td) 1t # 3c 1 # dt 23. x (x in y)# b cx 2) c y # "Î# c"Î# sin a)# b sin a# ) # c"Î# cos 20. qœ sÈa) c(r# sin a2r)(2) # b (cos 2)) acos " ) 2rbc r#)bœ c2 dr % 2r c r# b (#)" a2r c cos (2))(2 c a) bœ " c r œ 2r œ c rb Ê dq œ # a b (2) †da œ # b 2) rdrb 2r) 11. c" ( S#tep 1: Ê ’ds œ 7 y) Š1 c dy ‹“ dr (x c y)# (2x)c# 2x c 2y dyc$ œ )c$Î% Ê d) œ c 3 )c(Î% È2r c r s œ Èt œ t#Î( x# dt c2 tc&Î( 12. r œ È) 2(x d b œd8 4 dy " 7 y2)( b ˆ4 c " ‰ d Ê dx œ 21 (3x c 2)' † dx b c dx c& (csin 2t) "d (2t) dx ˆ4 c dx cos c& † dt (1 b cos 2t) œ c4(1(3xcos2) b3.61) ˆ4 c †#x ‰ †œ (1 bsin 2t x ‰ 2t) # Sectiondy(c Implicit Differentiation # " 161 È t œ c4(1 b #x 2t) dt # " cos 2t) dr ‰ 36. c#œ Šsec È)‹# (x c"y) Ê b 2y œ sec2x c 2x#d c) y)ˆc 2x(x c y) ˆ d Šsec 4) tan È)‹4Š " ‹ rˆ œ Step"2: c2x tan ˆ dy dy d ds Š œ È)‹ ˆ sec ‰ c " ‰ b tan ‰ (x #Î$ c 2)' c dx " )' † 3 b (c1) ˆ4 y œ "sinsˆœ x4 ‰ sinc3t b 54 cos 5t cos)ˆdt dxb345)cos 3t †† ˆdt (3t) (2t 54 )(csin 5t) †œ c 4 (2t b cos &Î$c 1 ˆ#È) b 5)c#Î$ ‰ 1œ 1 1 13. c 21. ‰ (2t3b 5) (3x‰ Ê# )dt œŠÊ (2t 1 c#Î$ ‰ c 2 ‰ b b 5)c&Î$ † 2 )dt (5t) œ 1 5)c3t cos sin 5t (2t #x 3 3 Rule and Parametric Equations dy x 4c ‹ 151 y dy cc (x c y) ˆ x œ c c ˆ Section 3.5 #The Chain c‰ y) c$ 4 3: dy c œ c21 1 b cot ˆ t ‰‰Step d cosbdxÈsin‰‰#œ"c2 b 2ydcot ˆ t"‰1c$ †È c y) È (x c d ˆ td‰...
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