Explanation Given information: The given function is f ( x ) = x − 1 x 2 + 1 . 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 ) = f ( x ) g ( x ) by Quotient Rule is, d d x [ f ( x ) g ( x ) ] = g ( x ) f ' ( x ) − f ( x ) g ' ( x ) [ g ( x ) ] 2 [ g ( x ) ≠ 0 ] Calculation: Differentiate the function f ( x ) = x − 1 x 2 + 1 with respect to x on both sides. f ′ ( x ) = d d x ( x − 1 x 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 11E

To determine

To find: The differential of a given function.

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Chapter 3.7, Problem 10E

Chapter 3.7, Problem 12E

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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 a given function.

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To find: The differential of a given function.

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Chapter 3 Solutions