Explanation Given information: The equation is, F ( x ) = f ( f ( x ) ) (1) Formula used: The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, h ′ ( x ) = d d x g [ f ( x ) ] = g ′ [ f ( x ) ] f ′ ( x ) Calculation: Differentiate equation (1) with respect to x by chain rule on both sides to calculate the value of F ′ ( x ) . F ′ ( x ) = d d x ( f ( f ( x ) ) ) = f ′ ( f ( x ) ) ⋅ d d x ( f ( x ) ) = f ′ ( f ( x ) ) ⋅ ( f ′ ( x ) ) (2) Take f ( x ) = x 2 . Since f ( x ) = x 2 , then f ′ ( x ) = d d x ( x 2 ) f ′ ( x ) = 2 x (3) Substitute x 2 for f ( x ) , 2 x for f ′ ( x ) in equation (2) to calculate the value of F ′ ( x )

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.3, Problem 60E

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Does it follow that F′(x)=[f′(x)]2 or not.

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Chapter 3.3, Problem 59E

Chapter 3.3, Problem 61E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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Does it follow that F ′ ( x ) = [ f ′ ( x ) ] 2 or not.

Solution Summary: The author explains that the formula to calculate the differential of a function h(x) = d

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Chapter 3 Solutions