Explanation Given information: The values of functions f and g and their derivatives are f ( 1 ) = 2 , f ′ ( 1 ) = − 1 , g ( 1 ) = − 2 and g ′ ( 1 ) = 3 . Formula used : The product rule of differentiation. The product rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Calculation: Use product rule of differentiation to get the derivative function h ′ ( x ) . h ′ ( x ) = d d x [ ( x 2 + 1 ) ⋅ g ( x ) ] = ( x 2 + 1 ) ⋅ d d x g ( x ) +

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.2, Problem 32E

To determine

To find: The value of derivative function h′(1) when the function h(x)=(x2+1)g(x) .

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Chapter 3.2, Problem 31E

Chapter 3.2, Problem 33E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The value of derivative function h ′ ( 1 ) when the function h ( x ) = ( x 2 + 1 ) g ( x ) .

Solution Summary: The author explains how to get the derivative function hprime '(1).

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To find: The value of derivative function h′(1) when the function h(x)=(x2+1)g(x) .

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Chapter 3 Solutions