Explanation Given information: Figures, Formula used: The chain rule, d d x h ( x ) = d d x ( f ( g ( x ) ) ) h ′ ( x ) = f ′ ( g ( x ) ) ⋅ g ′ ( x ) Calculation: Consider the derivative d d x g ( f ( x ) ) | x = 60 . Use the chain rule and find the derivative as below. d d x g ( f ( x ) ) = g ′ ( f ( x ) ) ⋅ f ′ ( x ) Substitute x = 60 into d d x g ( f ( x ) ) = g ′ ( f ( x ) ) ⋅ f ′ ( x ) . Thus, d d x g ( f ( 60 ) ) = g ′ ( f ( 60 ) ) ⋅ f ′ ( 60 ) ; f ( 60 ) = 20 = g ′ ( 20 ) ⋅ f ′ ( 60 ) Use the find the slope of the line to determine the value of g ′ ( 20 ) and f ′ ( 60 ) . From the graph of f ( x )

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 3.3, Problem 50P

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The derivative ddxg(f(x))|x=60.

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Chapter 3.3, Problem 49P

Chapter 3.3, Problem 51P

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Chapter 3 Solutions

APPLIED CALCULUS (WILEY PLUS)

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