Explanation Given information: The given function is f ( x ) = 3 x 2 − x . Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 g ′ ( x ) The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, d d x g [ f ( x ) ] = g ' [ f ( x ) ] ⋅ f ' ( x ) Calculation: Differentiate the given function with respect to x on both sides. f ′ ( x ) = d d x ( 3 x 2 − x ) = d d x [ ( 3 x 2 − x ) 1 2 ] = ( 1 2 ) ⋅ ( 3 x 2 − x ) 1 2 − 1

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 3.7, Problem 13E

To determine

To find: The differential of the given function.

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Chapter 3.7, Problem 12E

Chapter 3.7, Problem 14E

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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 differential of the given function.

Solution Summary: The author explains how to calculate the differential of a given function with respect to x on both sides.

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To find: The differential of the given function.

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Chapter 3 Solutions