Explanation Given information: The values of function f and its derivative is f ( 2 ) = 3 , f ′ ( 2 ) = − 1 and the function is g ( x ) = x 2 f ( x ) . Formula used: 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 the product rule of differentiation for the given function to get the derivative function g ′ ( x ) . g ′ ( x ) = d d x [ x 2 f ( x ) ] = x 2 ⋅ d d x f ( x ) + f ( 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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Question

Chapter 3.2, Problem 43E

To determine

To evaluate: The derivative function g′(2) when the function g(x)=x2f(x) .

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Chapter 3.2, Problem 42E

Chapter 3.2, Problem 44E

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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 derivative function g ′ ( 2 ) when the function g ( x ) = x 2 f ( x ) .

Solution Summary: The author evaluates the derivative function gprime '(2)' and its derivative by using the product rule of differentiation for the given function.

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To evaluate: The derivative function g′(2) when the function g(x)=x2f(x) .

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Chapter 3 Solutions