Explanation Given: Function f ( x , y ) = 2 x y ; y ≠ 0 . 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 ) = 2 x y ; y ≠ 0 . Differentiate f ( x , y ) with respect to x , we get ∂ f ∂ x = ∂ ∂ x ( 2 x y ) f x = ( 2 y ) ∂ ∂ x ( x ) f x = ( 2 y ) ( 1 ) f x = 2 y Differentiate f ( x , y ) with respect to y , we get ∂ f ∂ y = ∂ ∂ y ( 2 x y ) f y = 2 x ∂ ∂ y ( 1 y ) f y = 2 x ( − 1 ) ( y − 2 ) f y = − 2 x y 2 Now, ∂ 2 f ∂ x 2 = f x x = ( f x ) x f x x = ∂ ∂ x ( 2 y ) f x x = ( 2 y ) ∂ ∂ x ( 1 ) f x x = ( 2 y ) ( 0 ) f x x = 0 ∂ 2 f ∂ y 2 = f y y = ( f y ) y

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

See similar textbooks

Question

Chapter 8.4, Problem 31P

To determine

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

f(x,y)=2xy;y≠0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 30P

Chapter 8.4, Problem 32P

Students have asked these similar questions

The cost (in dollars) of manufacturing one item is given by C(x, y) = 70 + 4x + 9y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $25, and the material costs $6 per pound, what is the cost of manufacturing one of these items? 2$ (b) Find the partial derivative of C with respect to x. Cx =

SOLVE STEP BY STEP IN DIGITAL FORMAT

The temperature of the air in Boise is given by the function f(t,h) = 0.01ht² - 0.12ht - 0.6h t² + 12t + 60 Where f is the temperature in degrees Fahrenheit, t is measured in hours (with t = 0 corresponding to 9 a.m.), and h is the height above sea level, measured in thousands of feet. Find all four second order partial derivatives: a. ft(t,h) = b. fth(t,h) = c. fht(t,h) = d. fnn(t,h) =

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 ) = 2 x y ; y ≠ 0 .

Solution Summary: The author explains how to find the 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)=2xy;y≠0.

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 ) = 2 x y ; y ≠ 0 .

Solution Summary: The author explains how to find the 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)=2xy;y≠0.

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)=2xy;y≠0.