2.2 The Product Rule

📖 Chapter 2 Derivatives
📄 Page 88
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86
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2
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88
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12

calcCh3a.4lectureTube

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1

1 Product Rule Proof

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Answer
⏱️ 5:230🎬 k9LR8gcFF4A
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2

2 Product Rule ex1

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⏱️ 0:500🎬 2D39snO7EcE
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3

3 Product Rule ex3 with given facts about values of the functions at particular points

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⏱️ 1:590🎬 VoZOndNuA_g
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4

4 Product Rule ex4 with given facts about values of the functions at particular points ex2

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Answer
⏱️ 1:180🎬 i5TOPTSxa80
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calcvecMcGraw2.2solutions

82 videos

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1

001. Q1a

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:380🎬 33TJNWNzVCc
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2

001. Q1b

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:370🎬 _Ts9twGr1Xk
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3

001. Q1c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:340🎬 nIJgv9EfEhs
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4

001. Q1d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:320🎬 T9XG3jmPGmU
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5

002. Q2a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:350🎬 pK1eAw44n5k
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6

002. Q2b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:360🎬 hyDYP332dwE
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7

002. Q2c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:320🎬 zRcV0pyMKjM
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8

002. Q2d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:360🎬 ySwYDPipJ_0
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9

002. Q2e

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:370🎬 y0HfOiwXBBE
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10

002. Q2f

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:510🎬 1uWoTQV0CCQ
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11

003. Q3a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:420🎬 kVDf8xqjhrM
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12

003. Q3b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:290🎬 abVFmFc-4-4
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13

003. Q3c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:410🎬 SUYsVJy-qco
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14

003. Q3d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:430🎬 E8BzPsWQabY
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15

003. Q3e

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 0:450🎬 oxmehXevUmQ
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16

004. Q4a

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.expanded.form.f'g+fg', find.f.g
🎓 Given expanded form of product rule, find f and g
⏱️ 0:440🎬 -mSvPSJzCdo
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17

004. Q4b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.expanded.form.f'g+fg', find.f.g
🎓 Given expanded form of product rule, find f and g
⏱️ 0:500🎬 bLPdFv-hJDs
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18

004. Q4c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.expanded.form.f'g+fg', find.f.g
🎓 Given expanded form of product rule, find f and g
⏱️ 0:430🎬 6XnhAF8xD_g
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19

004. Q4d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.expanded.form.f'g+fg', find.f.g
🎓 Given expanded form of product rule, find f and g
⏱️ 1:010🎬 5N0cuSHDEP0
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20

005. Q5a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 1:330🎬 9HtL2igKwIA
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21

005. Q5b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 1:370🎬 B7jHfBdzrXI
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22

005. Q5c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 1:050🎬 qDAd4YlobR0
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23

005. Q5d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 1:510🎬 BmTcpE_ECi0
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24

005. Q5e

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 1:200🎬 lLJ4GrwNCK0
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25

005. Q5f

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 2:060🎬 8-NQnKnl8iE
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26

006. Q6a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 4:030🎬 3w8Z4DSB1hM
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27

006. Q6b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 2:410🎬 rluVZJXNkuw
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28

006. Q6c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 2:380🎬 4umWE2svb40
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29

006. Q6d

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 5:360🎬 o1O5PLNqMEQ
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30

007. Q7a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.lin.lin, differentiate
🎓 001. Product Rule with Linear Linear
⏱️ 2:420🎬 v1gTBF96yTw
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31

007. Q7b

Question
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given Functions and Point, find Tangent
🎓 001. Product Rule with Linear Linear
⏱️ 2:350🎬 K6cwZvK3PHE
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32

007. Q7c

Question
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given Functions and Point, find Tangent
🎓 001. Product Rule with Linear Linear
⏱️ 3:550🎬 Cnvkfpk25e0
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33

007. Q7d

Question
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given Functions and Point, find Tangent
🎓 001. Product Rule with Linear Linear
⏱️ 3:210🎬 XMBS0AG4O_E
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34

008. Q8b

Question
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Population.Growth
🎓 001. Population growth IROC
⏱️ 1:370🎬 Pj-vJKjp1Yo
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35

008. Q8c

Question
⏱️ 0:380🎬 Pj-vJKjp1Yo
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36

009. Q9a

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 0:520🎬 q2-5mMkEC70
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37

009. Q9b

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.algebraic.algebraic, differentiate
🎓 001. Product Rule with Negative Powers
⏱️ 1:570🎬 g7sh2MbZDBk
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38

009. Q9c

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Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 3:040🎬 XDIwUcbHpUg
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39

009. Q9d

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Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 2:230🎬 6gtZtIqN05g
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40

009. Q9e

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Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 1:510🎬 VGMd-vuKgEg
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41

010. Q10a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 2:180🎬 _rupVHYYfS8
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42

010. Q10b

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:510🎬 l7HdPsJGL_E
▶ Watch
43

010. Q10c

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 1:340🎬 zm5fawadlE8
▶ Watch
44

010. Q10d

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Answer
⏱️ 2:230🎬 6gtZtIqN05g
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45

010. Q10e

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Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 1:510🎬 VGMd-vuKgEg
▶ Watch
46

011. Q11a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:490🎬 UFet8LrK0mo
▶ Watch
47

011. Q11b

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 1:020🎬 owznnCmlNcA
▶ Watch
48

011. Q11c

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:360🎬 tmxesE_Hqyw
▶ Watch
49

011. Q11d

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:520🎬 sbLKkyBTubs
▶ Watch
50

011. Q11e

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 1:130🎬 KCVYFggFDMQ
▶ Watch
51

012. Q12

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given Functions and Point, find Tangent
🎓 001. Product Rule with Linear Linear
⏱️ 3:180🎬 xqhU97C-Nak
▶ Watch
52

013. Q13

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 4:410🎬 91h__2jXtcQ
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53

014. Q14a

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Answer
⏱️ 0:340🎬 X-ojRv5Ubvg
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54

014. Q14b

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Answer
⏱️ 2:500🎬 X-ojRv5Ubvg
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55

014. Q14c

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Answer
⏱️ 2:500🎬 X-ojRv5Ubvg
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56

015. Q15a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Population.Growth
🎓 001. Population growth IROC
⏱️ 0:420🎬 ndgBPs1_rKw
▶ Watch
57

015. Q15b

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Population.Growth
🎓 001. Population growth IROC
⏱️ 1:560🎬 dUGiT6VeoRo
▶ Watch
58

015. Q15c

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Population.Growth
🎓 001. Population growth IROC
⏱️ 3:290🎬 tCHpK1YVm-g
▶ Watch
59

015. Q15d

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Population.Growth
🎓 001. Population growth IROC
⏱️ 2:360🎬 ya9U7FfyIN0
▶ Watch
60

016. Q16a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:310🎬 IHKSHqqxThU
▶ Watch
61

016. Q16b

Question
Answer
⏱️ 2:220🎬 NrKEe0gMUws
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62

016. Q16c

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:320🎬 8It5z-5J1J4
▶ Watch
63

016. Q16d

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 3:370🎬 RnPQG6Xa4Mc
▶ Watch
64

016. Q16e

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 1:090🎬 RU95YKtw348
▶ Watch
65

016. Q16f

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:310🎬 3BQz2iTeNtI
▶ Watch
66

017. Q17a

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 2:380🎬 F3jIlpCqmUc
▶ Watch
67

017. Q17b

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 0:360🎬 u1dYmoL3S0M
▶ Watch
68

017. Q17cd

Question
Answer
⏱️ 1:150🎬 l4xRbUCQyfQ
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69

018. Q18a

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.fg,function.notation.form differentiate
🎓 001. Finding derivative of fg
⏱️ 1:470🎬 ts0g4m4R2po
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70

018. Q18b

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.poly.poly, differentiate
🎓 001. Product Rule Example
⏱️ 4:350🎬 0W-6GTyKqcc
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71

018. Q18cd

Question
Answer
📚 Related Lectures
13.2.1 CALCULUS, POWER RULE, given.Product, expand.differentiate
🎓 002. Expand to use power rule of binomial
🎓 001. Distribute to use Power Rule of Derivative
⏱️ 3:200🎬 o4vKHmmf4fA
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72

019. Q19a

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 1:050🎬 mdhQYi7_5nY
▶ Watch
73

019. Q19bc

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 1:120🎬 HbRunU6ZJ1Q
▶ Watch
74

020. Q20a

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.fg,function.notation.form differentiate
🎓 001. Finding derivative of fg
⏱️ 0:260🎬 naQ_lCMYKnU
▶ Watch
75

020. Q20b

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.fg,function.notation.form differentiate
🎓 001. Finding derivative of fg
⏱️ 0:330🎬 2elCncjukhc
▶ Watch
76

020. Q20c

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.fg,function.notation.form differentiate
🎓 001. Finding derivative of fg
⏱️ 0:440🎬 C-MzoB2y-zQ
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77

020. Q20d

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, CHAIN RULE, product.power
🎓 002. product power chain rule then evaluate
🎓 001. Differentiating Product Chain rule case
⏱️ 0:570🎬 MEY2rxV2ysg
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78

021. Q21a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, CHAIN RULE, differentiate.wrt.given.functions
🎓 001. Derivative using Chain Rule wrt f notation
⏱️ 1:190🎬 4C_cTbe_j_o
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79

021. Q21b

Question
Answer
📚 Related Lectures
13.2.3 Calculus, Chain Rule, power.power
🎓 001. Chain Rule, Power of Power
⏱️ 1:210🎬 jGFhmw47JqQ
▶ Watch
80

022. Q22

Question
Answer
📚 Related Lectures
13.2.2 CALCULUS, PRODUCT RULE, given.expanded.form.f'g+fg', find.f.g
🎓 Given expanded form of product rule, find f and g
⏱️ 2:030🎬 jj1YB923zCw
▶ Watch
81

023. Q23

Question
Answer
⏱️ 2:290🎬 hH3AFITrs_c
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82

08. Q8a

Question
Answer
📚 Related Lectures
13.2.4 CALCULUS, MODELLING with INSTANTANEOUS RATE OF CHANGE, given.Cost.Problem, find.f'
🎓 001. Marginal Profits
⏱️ 0:390🎬 HixsYBGsGbs
▶ Watch