Explanation Given: The function, y = 2 x x 2 + 1 . 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 Exponent rule: a n = a 1 / n , 1 a − n = a n 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 product rule and chain rule of derivatives and simplify further to get y ' = d d x ( 2 x x 2 + 1 ) = 2 x ⋅ d d x ( x 2 + 1 ) + x 2 + 1 ⋅ d d x ( 2 x ) = 2 x ⋅ d d x ( x 2 + 1 )

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3, Problem 19E

To determine

The derivative y' of the function, y=2xx2+1 .

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Chapter 3, Problem 18E

Chapter 3, Problem 20E

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The derivative y ' of the function, y = 2 x x 2 + 1 .

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

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The derivative y' of the function, y=2xx2+1 .

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