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: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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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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From a function f(x) = 5000 x2 - 7000x + 12000 Find the first and second derivatives

If f(x) = 4x²x³, find f'(x), f"(x), F"(x), and f(4)(x). f'(x) = H F"(x) = f(x) = f(4)(x) = Graph f, f', f", and f"" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? The graphs-Select- consistent with the geometric interpretations of the derivatives because f-Select--- f' has a slope of m= 0, and fis-Select-- function equal to the slope of f". Need Help? Read It Submit Answer O Type here to search Tab k 4 Caps Lock F1 ! 1 F2 A 2 Watch It F3 # 3 WE S O X F4 View Previous Question Question 6 of 10 View Next Question Cheapest Online Mba Programs - Search On Our Website 0 D $ 4 D R C M % 5 F 14 F6 T 6 F7 G Y FB H 8 1 where f has a slope of m= 0, f"-Select- 84°F Sunny 100 5 O F11 Activate Windows Go to Settings to activate Windows 0 BN MO P J K 2 L de ENG where 6:55 PM 9/19/2022 C

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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)).

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Chapter 3 Solutions

To calculate:

The derivative h′(1) if h(x)=f(g(x)).