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## Week 5 Lecture Notes

by: Monica Weisenbach

42

0

2

# Week 5 Lecture Notes MATH127

Monica Weisenbach
UMass
GPA 3.819
Calculus I for Life and Social Science Majors
Thurlow Cook

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Technically, it's the seventh week but only the 5th week of real notes. It covers the chain rule and product rule for derivatives, including a list of example problems with answers.
COURSE
Calculus I for Life and Social Science Majors
PROF.
Thurlow Cook
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
UMass, amherst, Umass Amherst, Math, Calculus, 127
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Monica Weisenbach on Friday March 6, 2015. The Class Notes belongs to MATH127 at University of Massachusetts taught by Thurlow Cook in Spring2015. Since its upload, it has received 42 views. For similar materials see Calculus I for Life and Social Science Majors in Mathematics (M) at University of Massachusetts.

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Date Created: 03/06/15
Week 5 Notes Chain Rule for Derivatives The chain rule is simply fgx f gxg x or vux v uxu x Please note that this can go further along as in hfgx The reason for this is that x is first modified by function g then it s all modified by function f M AV AU Because the change in V depends on the change in U AX AU AX which depends on the change in X Take yx21 5 what s y y 5X2142X 5X214 is f gx and 2X is g x Car example gallons of fuel used per time depends on gallons of fuel used per speed and speed per time Examples y X215 f gXg x 5X214 2X lOXX214 y lnx2 l f gXg x 1X212X 2XX21 Product Rule The product rule is simply fg x f g g f A proof of this rule is below i AX gx M 3 F 3 AX ox 1 M m Ax fax i 39A X X AX 1 Rmbx bf Fa aka in ra Examples y xeX aka fx x and gx ex f 9f9 1eX xeX eXx1 y x2X3 aka fX X2 and gx x3 f gfg 2X X3 X23X2 2X4 3X4 5X4 Examples Find the Derivatives Answers 1 yX31 Y 3X2 2VX31 2 y5ln1eX y 5eX 1eX 3 yln2x y 1 2X1ln2x 4 yx4x2113 y 4X32X 3xx4x2113 5 yn3x22 y 6X 3X22 6 yeX y eVX 2xx 7 y8eX y 4eVX X 8 ye8X y 4e8VX xx Hint Some of these problems use both the Chain rule and the product rule Problem 3 is one of them

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