circuit’training–’productandquotientrules...

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Circuit Training – Product and Quotient Rules Name ______________________________ Directions: Begin in cell #1. Find the derivative. Search for your answer, and then call that cell #2. Proceed in this manner until you complete the circuit. You may need to attach additional sheets to show your best work. Answer: ! ! ! # ___1___ ! = (2! 5)(3! + 7) Answer: !! ! !!"!!! ! ! # _______ ! = cos ! ! Answer: sec ! ! # _______ ! = !!!! ! ! Answer: ! (!!!!) ! # _______ ! = !!!"# ! !!!"# ! Answer: !!! !"# !!!"# !! ! ! !"# ! !"# ! ! # _______ ! = ! ! !!!! Answer: ! ! ! ! !! ! ! + !" !" # _______ ! = ! (! + 3) ! Answer: 12! 1 # _______ ! = !!!! !!!! Answer: sec ! tan ! # _______ Given ! 5 = 3, ! ! 5 = 3! + 7, ! 5 = 2! 1, ! ! 5 = ! ! . If ! = ! ! ! ! , calculate ! 5 . Answer: !!(!!!!) ! ! # _______ ! = !!!! ! Answer: 2 sin ! cos ! # _______ ! = tan ! (HINT: Rewrite as !"# ! !"# ! . ) © Virge Cornelius 2016 16 cos xJ y 2 3 7 2 5 3 y 2kosxj C Sina 6 14 6 5 y 2sinxcosx y e2x I y 3L x2 y L sinxsci is.mx Uecosx cos q xD Cesinxj y 3 3 9 3 1 2 6 yia s.nx sinx cosx.co 6 yes.mx y icsinxecosx csinzxec.sk y 6 3 1 2 3 42 7 Cesinxja 6 y 3 11 y Csinxecosx smx 15 y 1 2 41 332 Tx 21 33 I y 217 1 35 2 6 Tx 35 2 6 9 c 4 2 1211 5 2 18 9 y are arx 2 12 y 213 7 2 5 s 34 D2 hilt fileget flag'LE Y 6 34176,2 157 mess f'es gcs s ifcs sg.es 3 7 2 1 36 y In a mix 3 7 1.5 6 75 6 2 11 5.5 ii sirs 37text y Sec x 8 O y's 3rx 35 29 cosx x cosx.cosx s.mx C sin y 6 6 7 y cosox 2 55 y cosaxesinox Seck y air

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Page 1: Circuit’Training–’ProductandQuotientRules ...smacmathapcalculus.weebly.com/uploads/1/9/2/5/...3 9 3 1 2 6 yia s.nx sinxcosx.co 6 yes.mx y icsinxecosx csinzxec.sk y 6 3 12 342

Circuit'Training'–'Product'and'Quotient'Rules'' ''''''''''''''''''''''Name'______________________________''Directions:++Begin+in+cell+#1.++Find+the+derivative.++Search+for+your+answer,+and+then+call+that+cell+#2.++Proceed+in+this+manner+until+you+complete+the+circuit.++You+may+need+to+attach+additional+sheets+to+show+your+best+work.++++Answer:+++++− !

!!++#+___1___+++++! = ! (2! − 5)(3! + 7)+++++

Answer:+++++!!!!!"!!!! ! ++#+_______+++++! = ! cos!!+++++

Answer:+++++sec!!++#+_______+++++! = ! !!!!!! +

Answer:+++++− !(!!!!)!+

+#+_______+++++! = ! !!!"#!!!!"#! ++++++

Answer:+++++!!! !"#!!!"#!!!!! !"#!!"#!! ++#+_______+++++! = ! !!

!!!!+

Answer:+++++− !! !

! − !!! ! +

!"!"+

+#+_______++++++! = ! !(! + 3)!++++++

Answer:+++++12! − 1++#+_______+++++! = ! !!!!!!!!'

Answer:+++++sec ! tan !++#+_______+++++Given+! 5 = 3, !!! 5 = 3! + 7,++++++++++++++++++++! 5 = !2! − 1, !!! 5 = ! !!+.+++++++++++++++++++++If+ℎ ! = !! ! ∙ ! ! , calculate!ℎ! 5 .++++++

Answer:+++++!!(!!!!)!! ++#+_______+++++! = ! !!!!! +

Answer:+++++2 sin ! cos !++#+_______+++++! = tan !++++++++++++++++++++(HINT:+Rewrite+as+!"#!!"#! . )+++++

©++Virge+Cornelius+2016+

16 cosxJ

y 2 3 7 2 5 3 y 2kosxjCSina6 14 6 5 y 2sinxcosx

y e2x I

y 3L x2 y Lsinxsciis.mx Uecosxcos

q xD Cesinxj

y 3 3 9 3 1 2 6 yia s.nx sinxcosx.co6 yes.mxy icsinxecosxcsinzxec.sk

y 6 3 12 342 7 Cesinxja6y 3 11 y

Csinxecosxsmx

15y 12 41 332 Tx 21 33 Iy 217 1 35 2 6 Tx 35

2 6 9 c 4 2 1211 5 2 18 9y are arx

2 12y 213 7 2 5 s

34D2 hilt fileget flag'LEY 6 34176,2157 mess f'esgcssifcssg.es

3 7 2 1 36y In a mix 3 7 1.56 75 6 2 11 5.5

ii sirs 3 7text y Sec x

8O y's 3rx 35 29 cosxx

cosx.cosx s.mxCsiny 6 6 7 y cosox2 55 y cosaxesinox Secky air

Page 2: Circuit’Training–’ProductandQuotientRules ...smacmathapcalculus.weebly.com/uploads/1/9/2/5/...3 9 3 1 2 6 yia s.nx sinxcosx.co 6 yes.mx y icsinxecosx csinzxec.sk y 6 3 12 342

Answer:+++++!(2 cos ! − ! sin !)++#+_______+++++! = ! sin !!++++++

Answer:+++++−2 sin ! cos !++#+_______+++++! = csc !+++++++

Answer:+++++6!! + 11! − !!! +

+#+_______+++++! = cot !+

Answer:+++++!!!!!! !++#+_______+++++! = sec !++++++++++++++++++++++(HINT:++Rewrite+this+trig+function.)+++++++

Answer:+++++!!!!!"!(!!!!)! ++#+_______+++++! = ! !!!!!!!! +++++

Answer:+++++− csc ! cot !++#+_______+++++! = ! !!!!!"#! +++++++

Answer:+++++! cos ! + sin !++#+_______+++++! = ! !

!!!!+'

Answer:+++++ !"(!!!!)!+

+#+_______+++++! = !!! cos !+++++++

Answer:+++++−csc!!++#+_______+++++Given+! 5 = 3, !!! 5 = 3! + 7,++++++++++++++++++++! 5 = !2! − 1, !!! 5 = ! !!+.+++++++++++++++++++++If+! ! = ! !(!)!(!) , calculate!!

! 5 .++++++

Answer:+++++− !"#!!!"#!!!(!!!"#!)! +

+#+_______+++++! = ! sin!!++++++++++++++++++++++(HINT:+Rewrite+as+sin !! ∙ sin ! ! . )+

©++Virge+Cornelius+2016+

4 17 ISinx

y sinx xcosxyinoishxg n.LI cosxsinTsinxcotxcscx

CoSx 13 It cosx

ySmx Smx cosxcosx o.cosx 1Cs.in

sink cosaxy t y off cotanxsecxScn2xycsc2xyi 2xKsinx Gxycosx

18 i 2xsinxg_gosx

S y 34 77

y L y's 2x cosx x'sinx3 7 2 y 2cosx xsinx

14 K'ltj 5 ffg.FI7 nxt

nothemes

Kys E 3 2 1 3 7 Ztaxiiiii.in y 2 sine osx5 a z

3 122 22 4 y 2sinxcosx8 is

32 Ig