a. Explanation Given: The function f is a differentiable function. And g ( x ) = [ f ( x ) ] 3 Formula Used: Product rule: Let f, g and h be differentiable functions. Then, ( f g h ) ′ = ( f ′ ) g h + f ( g ′ ) h + f g ( h ′ ) Consider, g ′ = [ f 3 ] ′ b. To determine To show: For p ( x ) = [ f ( x ) ] 4 , its derivative is p ′ ( x ) = 4 [ f ( x ) ] 3 f ′ ( x )

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.2, Problem 59PS

To determine

To show:For g(x)=[f(x)]3 , its derivative is g′(x)=3[f(x)]2f′(x) .

To determine

To show: For p(x)=[f(x)]4 , its derivative is p′(x)=4[f(x)]3f′(x)

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Chapter 3.2, Problem 58PS

Chapter 3.2, Problem 60PS

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Chapter 3 Solutions

Calculus

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For g ( x ) = [ f ( x ) ] 3 , its derivative is g ′ ( x ) = 3 [ f ( x ) ] 2 f ′ ( x ) .

Solution Summary: The author explains that the function f is a differentiable function.

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To show:For g(x)=[f(x)]3 , its derivative is g′(x)=3[f(x)]2f′(x) .

To show: For p(x)=[f(x)]4 , its derivative is p′(x)=4[f(x)]3f′(x)

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Chapter 3 Solutions