Explanation Given: The function, sin ( x y ) = x 2 − y . 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 d d x ( sin x ) = cos x d d x ( cos x ) = − sin 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 product rule and chain rule of derivatives and differentiate implicitly with respect to x to get d d x ( sin ( x y ) ) = d d x ( x 2 − y ) cos ( x y ) ⋅ d d x ( x y ) = d d x ( x 2 ) −

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3, Problem 35E

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The derivative y' of the function, sin(xy)=x2−y .

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Chapter 3, Problem 34E

Chapter 3, Problem 36E

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Chapter 3 Solutions

Biocalculus

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The derivative y ' of the function, sin ( x y ) = x 2 − y .

Solution Summary: The author explains the product rule and chain rule of derivatives and differentiate implicitly with respect to x to find the derivative of the function.

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The derivative y' of the function, sin(xy)=x2−y .

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Chapter 3 Solutions