Explanation Given: The given function is 5 x y 2 = 10 , d x d t = − 2 and x = 1 . Concept Used: The product rule of derivative is, d d x ( f ( x ) g ( x ) ) = f ( x ) d d x ( g ( x ) ) + g ( x ) d d x ( f ( x ) ) Calculation: The given expression is 5 x y 2 = 10 . Apply product rule to find the derivative with respect to t. d d t ( 5 x y 2 ) = d d t ( 10 ) 5 x d d t ( y 2 ) + 5 y 2 d d t ( x ) = 0 5 x × 2 y d y d t + 5 y 2 d x d t = 0 Substitute 1 for x and − 2 for d x d t in the above equation to find d y d t

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 3.7, Problem 19PS

To determine

The rate of the given function.

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Chapter 3.7, Problem 18PS

Chapter 3.7, Problem 20PS

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Chapter 3 Solutions

Calculus

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The rate of the given function.

Solution Summary: The author calculates the rate of the given function, which is 5xy2=10, and applies the product rule to find the derivative with respect to t.

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The rate of the given function.

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Chapter 3 Solutions