Explanation Given: Function f ( x , y ) = 5 + x 2 y 2 . Formula Used: Formula of second-order partial derivatives are as follows: ∂ 2 f ∂ x 2 = f x x = ( f x ) x ∂ 2 f ∂ y 2 = f y y = ( f y ) y ∂ 2 f ∂ x ∂ y = f y x = ( f y ) x ∂ 2 f ∂ y ∂ x = f x y = ( f x ) y Calculation: Function is given as f ( x , y ) = 5 + x 2 y 2 . Differentiate f ( x , y ) with respect to x , we get ∂ f ∂ x = ∂ ∂ x ( 5 + x 2 y 2 ) f x = ∂ ∂ x ( 5 ) + ∂ ∂ x ( x 2 y 2 ) f x = 0 + y 2 ∂ ∂ x ( x 2 ) f x = y 2 ( 2 x ) f x = 2 x y 2 Differentiate f ( x , y ) with respect to y , we get ∂ f ∂ y = ∂ ∂ y ( 5 + x 2 y 2 ) f y = ∂ ∂ y ( 5 ) + ∂ ∂ y ( x 2 y 2 ) f y = 0 + x 2 ∂ ∂ y ( y 2 ) f y = x 2 ( 2 y ) f y = 2 x 2 y Now, ∂ 2 f ∂ x 2 = f x x = ( f x ) x f x x = ∂ ∂ x ( 2 x y 2 ) f x x

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

See similar textbooks

Question

Chapter 8.4, Problem 32P

To determine

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal.

f(x,y)=5+x2y2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 31P

Chapter 8.4, Problem 33P

Students have asked these similar questions

Solve for the derivatives of the following function. 1. y = 4x3 -7x- 2. у %3 3 3. y = xVx 4. y = 3x? - 5x+2 5. y = -14x-10

I. Find the derivatives of the following functions: 1. f(x) = v2x+ + 3 2. f(x) = (2 x? + 5)-4 (4 x5 + 1) 2x5+1 (-2x2-5)-41 3. f(x)

If the value of bo is negative, then the relationship: will not cause any impact to y values regardless of how the x values change. cannot be determined by this alone causes y to increase as x increases. causes y to decrease as x increases.

Chapter 8 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Prob. 3P Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.1 - Prob. 10P

Ch. 8.1 - Prob. 11P Ch. 8.1 - Prob. 12P Ch. 8.1 - Prob. 13P Ch. 8.1 - Prob. 14P Ch. 8.1 - Prob. 15P Ch. 8.1 - Prob. 16P Ch. 8.1 - Prob. 17P Ch. 8.1 - Prob. 18P Ch. 8.1 - Prob. 19P Ch. 8.1 - Prob. 20P Ch. 8.1 - Prob. 21P Ch. 8.1 - Prob. 22P Ch. 8.1 - Prob. 23P Ch. 8.1 - Prob. 24P Ch. 8.1 - Prob. 25P Ch. 8.1 - Prob. 26P Ch. 8.1 - Prob. 27P Ch. 8.1 - Prob. 28P Ch. 8.1 - Prob. 29P Ch. 8.1 - Prob. 30P Ch. 8.2 - Prob. 1P Ch. 8.2 - Prob. 2P Ch. 8.2 - Prob. 3P Ch. 8.2 - Prob. 4P Ch. 8.2 - Prob. 5P Ch. 8.2 - Prob. 6P Ch. 8.2 - Prob. 7P Ch. 8.2 - Prob. 8P Ch. 8.2 - Prob. 9P Ch. 8.2 - Prob. 10P Ch. 8.2 - Prob. 11P Ch. 8.2 - Prob. 12P Ch. 8.2 - Prob. 13P Ch. 8.2 - Prob. 14P Ch. 8.2 - Prob. 15P Ch. 8.2 - Prob. 16P Ch. 8.2 - Prob. 17P Ch. 8.2 - Prob. 18P Ch. 8.2 - Prob. 19P Ch. 8.2 - Prob. 20P Ch. 8.2 - Prob. 21P Ch. 8.2 - Prob. 22P Ch. 8.2 - Prob. 23P Ch. 8.2 - Prob. 24P Ch. 8.2 - Prob. 25P Ch. 8.2 - Prob. 26P Ch. 8.2 - Prob. 27P Ch. 8.2 - Prob. 28P Ch. 8.2 - Prob. 29P Ch. 8.2 - Prob. 30P Ch. 8.2 - Prob. 31P Ch. 8.2 - Prob. 32P Ch. 8.2 - Prob. 33P Ch. 8.2 - Prob. 34P Ch. 8.2 - Prob. 35P Ch. 8.2 - Prob. 36P Ch. 8.2 - Prob. 37P Ch. 8.2 - Prob. 38P Ch. 8.2 - Prob. 39P Ch. 8.2 - Prob. 40P Ch. 8.2 - Prob. 41P Ch. 8.2 - Prob. 42P Ch. 8.2 - Prob. 43P Ch. 8.2 - Prob. 44P Ch. 8.3 - Prob. 1P Ch. 8.3 - Prob. 2P Ch. 8.3 - Prob. 3P Ch. 8.3 - Prob. 4P Ch. 8.3 - Prob. 5P Ch. 8.3 - Prob. 6P Ch. 8.3 - Prob. 7P Ch. 8.3 - Prob. 8P Ch. 8.3 - Prob. 9P Ch. 8.3 - Prob. 10P Ch. 8.3 - Prob. 11P Ch. 8.3 - Prob. 12P Ch. 8.3 - Prob. 13P Ch. 8.3 - Prob. 14P Ch. 8.3 - Prob. 15P Ch. 8.3 - Prob. 16P Ch. 8.3 - Prob. 17P Ch. 8.3 - Prob. 18P Ch. 8.3 - Prob. 19P Ch. 8.3 - Prob. 20P Ch. 8.3 - Prob. 21P Ch. 8.3 - Prob. 22P Ch. 8.3 - Prob. 23P Ch. 8.3 - Prob. 24P Ch. 8.3 - Prob. 25P Ch. 8.3 - Prob. 26P Ch. 8.3 - Prob. 27P Ch. 8.3 - Prob. 28P Ch. 8.3 - Prob. 29P Ch. 8.3 - Prob. 30P Ch. 8.3 - Prob. 31P Ch. 8.3 - Prob. 32P Ch. 8.3 - Prob. 33P Ch. 8.3 - Prob. 34P Ch. 8.3 - Prob. 35P Ch. 8.3 - Prob. 36P Ch. 8.3 - Prob. 37P Ch. 8.3 - Prob. 38P Ch. 8.3 - Prob. 39P Ch. 8.3 - Prob. 40P Ch. 8.4 - Prob. 1P Ch. 8.4 - Prob. 2P Ch. 8.4 - Prob. 3P Ch. 8.4 - Prob. 4P Ch. 8.4 - Prob. 5P Ch. 8.4 - Prob. 6P Ch. 8.4 - Prob. 7P Ch. 8.4 - Prob. 8P Ch. 8.4 - Prob. 9P Ch. 8.4 - Prob. 10P Ch. 8.4 - Prob. 11P Ch. 8.4 - Prob. 12P Ch. 8.4 - Prob. 13P Ch. 8.4 - Prob. 14P Ch. 8.4 - Prob. 15P Ch. 8.4 - Prob. 16P Ch. 8.4 - Prob. 17P Ch. 8.4 - Prob. 18P Ch. 8.4 - Prob. 19P Ch. 8.4 - Prob. 20P Ch. 8.4 - Prob. 21P Ch. 8.4 - Prob. 22P Ch. 8.4 - Prob. 23P Ch. 8.4 - Prob. 24P Ch. 8.4 - Prob. 25P Ch. 8.4 - Prob. 26P Ch. 8.4 - Prob. 27P Ch. 8.4 - Prob. 28P Ch. 8.4 - Prob. 29P Ch. 8.4 - Prob. 30P Ch. 8.4 - Prob. 31P Ch. 8.4 - Prob. 32P Ch. 8.4 - Prob. 33P Ch. 8.4 - Prob. 34P Ch. 8.4 - Prob. 35P Ch. 8.4 - Prob. 36P Ch. 8.4 - Prob. 37P Ch. 8.4 - Prob. 38P Ch. 8.4 - Prob. 39P Ch. 8.4 - Prob. 40P Ch. 8.4 - Prob. 41P Ch. 8.4 - Prob. 42P Ch. 8.4 - Prob. 43P Ch. 8.4 - Prob. 44P Ch. 8.5 - Prob. 1P Ch. 8.5 - Prob. 2P Ch. 8.5 - Prob. 3P Ch. 8.5 - Prob. 4P Ch. 8.5 - Prob. 5P Ch. 8.5 - Prob. 6P Ch. 8.5 - Prob. 7P Ch. 8.5 - Prob. 8P Ch. 8.5 - Prob. 9P Ch. 8.5 - Prob. 10P Ch. 8.5 - Prob. 11P Ch. 8.5 - Prob. 12P Ch. 8.5 - Prob. 13P Ch. 8.5 - Prob. 14P Ch. 8.5 - Prob. 15P Ch. 8.5 - Prob. 16P Ch. 8.5 - Prob. 17P Ch. 8.5 - Prob. 18P Ch. 8.5 - Prob. 19P Ch. 8.5 - Prob. 20P Ch. 8.5 - Prob. 21P Ch. 8.5 - Prob. 22P Ch. 8.5 - Prob. 23P Ch. 8.5 - Prob. 24P Ch. 8.5 - Prob. 25P Ch. 8.5 - Prob. 26P Ch. 8.5 - Prob. 27P Ch. 8.5 - Prob. 28P Ch. 8.5 - Prob. 29P Ch. 8.5 - Prob. 30P Ch. 8.5 - Prob. 31P Ch. 8.5 - Prob. 32P Ch. 8.6 - Prob. 1P Ch. 8.6 - Prob. 2P Ch. 8.6 - Prob. 3P Ch. 8.6 - Prob. 4P Ch. 8.6 - Prob. 5P Ch. 8.6 - Prob. 6P Ch. 8.6 - Prob. 7P Ch. 8.6 - Prob. 8P Ch. 8.6 - Prob. 9P Ch. 8.6 - Prob. 10P Ch. 8.6 - Prob. 11P Ch. 8.6 - Prob. 12P Ch. 8.6 - Prob. 13P Ch. 8.6 - Prob. 14P Ch. 8.6 - Prob. 15P Ch. 8.6 - Prob. 16P Ch. 8.6 - Prob. 17P Ch. 8.6 - Prob. 18P Ch. 8.6 - Prob. 19P Ch. 8.6 - Prob. 20P Ch. 8.6 - Prob. 21P Ch. 8.6 - Prob. 22P Ch. 8.6 - Prob. 23P Ch. 8.6 - Prob. 24P Ch. 8.6 - Prob. 25P Ch. 8.6 - Prob. 26P Ch. 8.6 - Prob. 27P Ch. 8 - Prob. 1SYU Ch. 8 - Prob. 2SYU Ch. 8 - Prob. 3SYU Ch. 8 - Prob. 4SYU Ch. 8 - Prob. 5SYU Ch. 8 - Prob. 6SYU Ch. 8 - Prob. 7SYU Ch. 8 - Prob. 8SYU Ch. 8 - Prob. 9SYU Ch. 8 - Prob. 10SYU Ch. 8 - Prob. 11SYU Ch. 8 - Prob. 12SYU Ch. 8 - Prob. 13SYU Ch. 8 - Prob. 14SYU Ch. 8 - Prob. 15SYU Ch. 8 - Prob. 16SYU Ch. 8 - Prob. 17SYU Ch. 8 - Prob. 18SYU Ch. 8 - Prob. 19SYU Ch. 8 - Prob. 20SYU Ch. 8 - Prob. 21SYU Ch. 8 - Prob. 22SYU Ch. 8 - Prob. 23SYU Ch. 8 - Prob. 24SYU Ch. 8 - Prob. 25SYU Ch. 8 - Prob. 26SYU Ch. 8 - Prob. 27SYU Ch. 8 - Prob. 28SYU Ch. 8 - Prob. 29SYU Ch. 8 - Prob. 30SYU Ch. 8 - Prob. 31SYU Ch. 8 - Prob. 32SYU Ch. 8 - Prob. 33SYU Ch. 8 - Prob. 34SYU Ch. 8 - Prob. 35SYU Ch. 8 - Prob. 36SYU Ch. 8 - Prob. 37SYU Ch. 8 - Prob. 38SYU Ch. 8 - Prob. 39SYU Ch. 8 - Prob. 40SYU Ch. 8 - Prob. 41SYU Ch. 8 - Prob. 42SYU Ch. 8 - Prob. 43SYU Ch. 8 - Prob. 44SYU Ch. 8 - Prob. 45SYU Ch. 8 - Prob. 46SYU Ch. 8 - Prob. 47SYU Ch. 8 - Prob. 48SYU Ch. 8 - Prob. 49SYU Ch. 8 - Prob. 50SYU Ch. 8 - Prob. 51SYU Ch. 8 - Prob. 52SYU Ch. 8 - Prob. 53SYU Ch. 8 - Prob. 54SYU Ch. 8 - Prob. 55SYU Ch. 8 - Prob. 56SYU Ch. 8 - Prob. 57SYU Ch. 8 - Prob. 58SYU Ch. 8 - Prob. 59SYU Ch. 8 - Prob. 60SYU Ch. 8 - Prob. 1FOT Ch. 8 - Prob. 2FOT Ch. 8 - Prob. 3FOT Ch. 8 - Prob. 4FOT Ch. 8 - Prob. 5FOT Ch. 8 - Prob. 6FOT Ch. 8 - Prob. 7FOT

Knowledge Booster

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. f ( x , y ) = 5 + x 2 y 2 .

Solution Summary: The author explains how to find all four second-order partial derivatives and confirm that the mixed partials are equal.

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal.

f(x,y)=5+x2y2.

Want to see the full answer?

Chapter 8 Solutions

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. f ( x , y ) = 5 + x 2 y 2 .

Solution Summary: The author explains how to find all four second-order partial derivatives and confirm that the mixed partials are equal.

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. f(x,y)=5+x2y2.

Want to see the full answer?

Chapter 8 Solutions

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal.

f(x,y)=5+x2y2.