Explanation Given: The function is f ( x , y ) = 1 x − 5 y 2 . Formula Used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 Calculation: Consider the following function, f ( x , y ) = 1 x − 5 y 2 Determine the derivative of function with respect to x . f x ( x , y ) = − 1 x 2 Here, consider y term to be constant and derivate with respect to x. Determine the derivative of function with respect to y . f y ( x , y ) = 10 y 3 Here, consider x term to be constant and derivate with respect to y. Now, determine second order partial derivatives of the provided function. Derivate f x ( x , y ) = − 1 x 2 with respect to x . f x x ( x , y ) = 2 x 3 Here, consider y term to be constant and derivate with respect to x. Derivate f x ( x , y ) = − 1 x 2 with respect to y , f x y ( x , y ) = 0 Here, consider x term to be constant and derivate with respect to y

12th Edition

ISBN: 8220106844557

Author: MULLINS

Publisher: PEARSON

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Chapter 14.2, Problem 21E

To determine

To calculate: The second order partial derivatives for the function f(x,y)=1x−5y2.

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Chapter 14.2, Problem 20E

Chapter 14.2, Problem 22E

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Chapter 14 Solutions

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Knowledge Booster

The second order partial derivatives for the function f ( x , y ) = 1 x − 5 y 2 .

Solution Summary: The author explains how to calculate the second order partial derivatives for the function f(x,y)=1x-

To calculate: The second order partial derivatives for the function f(x,y)=1x−5y2.

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Chapter 14 Solutions