Explanation Given: The function, y = e x 1 + x 2 . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 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 d d x ( e x ) = e x 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 quotient rule and chain rule of derivatives and simplify further to get y ' = d d x ( e x 1 + x 2 ) = ( 1 + x 2 ) ⋅ d d x ( e x ) − ( e x

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3, Problem 20E

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The derivative y' of the function, y=ex1+x2 .

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Chapter 3, Problem 19E

Chapter 3, Problem 21E

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Chapter 3 Solutions

Biocalculus

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

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

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Chapter 3 Solutions