Explanation Given: The function, f ( x ) = x 2 g ( x ) . Concept Used: The product rule of derivatives: d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: In order to find the derivative of the function, use chain rule andproduct rule of derivatives and simplify further to get d d x ( f ( x ) ) = d d x ( x 2 g (

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3, Problem 63E

To determine

The derivative f' in terms of g' for, f(x)=x2g(x) .

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Chapter 3, Problem 62E

Chapter 3, Problem 64E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The derivative f ' in terms of g ' for, f ( x ) = x 2 g ( x ) .

Solution Summary: The author explains how to find the derivative of the function using chain rule and product rule of derivatives.

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The derivative f' in terms of g' for, f(x)=x2g(x) .

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Chapter 3 Solutions