Explanation Given information: The figures as shown below. 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 function h ( x ) = f ( g ( x ) ) . Find the first derivative with respect to x as below. Thus, d d x h ( x ) = d d x ( f ( g ( x ) ) ) h ′ ( x ) = f ′ ( g ( x ) ) ⋅ g ′ ( x ) Substitute x = 1 into h ′ ( x ) = f ′ ( g ( x ) ) ⋅ g ′ ( x ) . Thus, h ′ ( x ) = f ′ ( g ( x ) ) ⋅ g ′ ( x ) h ′ ( 1 ) = f ′ ( g ( 1 ) ) ⋅ g ′ ( 1 ) g ( 1 ) = 3 h ′ ( 1 ) = f ′ ( 3 ) ⋅ g ′ ( 1 ) … ( 1 ) Sketch lines on the graph as below. Consider the section of the graph as a straight line to estimate the slope. The slope of the line. m = y 2 − y 1 x 2 − x 1 = 1

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 3.3, Problem 41P

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The derivative h′(1) if h(x)=f(g(x)).

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Chapter 3.3, Problem 40P

Chapter 3.3, Problem 42P

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The derivative h ′ ( 1 ) if h ( x ) = f ( g ( x ) ) .

Solution Summary: The author explains how to calculate the derivative hprime(1)is1.5.

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To calculate:

The derivative h′(1) if h(x)=f(g(x)).

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Chapter 3 Solutions

The derivative h ′ ( 1 ) if h ( x ) = f ( g ( x ) ) .

Solution Summary: The author explains how to calculate the derivative hprime(1)is1.5.

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To calculate: The derivative h′(1) if h(x)=f(g(x)).

Want to see the full answer?

Chapter 3 Solutions

To calculate:

The derivative h′(1) if h(x)=f(g(x)).