Explanation Given: Function P = 2 K L 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 P = 2 K L 2 . Differentiate P with respect to K , we get ∂ P ∂ K = ∂ ∂ K ( 2 K L 2 ) P K = 2 L 2 ∂ ∂ K ( K ) P K = 2 L 2 ( 1 ) P K = 2 L 2 Differentiate P with respect to L , we get ∂ P ∂ L = ∂ ∂ L ( 2 K L 2 ) P L = 2 K ∂ ∂ L ( L 2 ) P L = 2 K ( 2 L ) P L = 4 K L Now, ∂ 2 P ∂ K 2 = P K K = ( P K ) K P K K = ∂ ∂ K ( 2 L 2 ) P K K = 2 L 2 ∂ ∂ K ( 1 ) P K K = 2 L 2 ( 0 ) P K K</

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 8.4, Problem 39P

To determine

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

P=2KL2

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Chapter 8.4, Problem 38P

Chapter 8.4, Problem 40P

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Chapter 8 Solutions

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Knowledge Booster

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. P = 2 K L 2

Solution Summary: The author explains that the four second-order partial derivatives are equal.

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

P=2KL2

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. P = 2 K L 2

Solution Summary: The author explains that the four second-order partial derivatives are equal.

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. P=2KL2

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.

P=2KL2