Explanation Given: Function f = 100 e r t . 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 = 100 e r t . Differentiate f with respect to r , we get ∂ f ∂ r = ∂ ∂ r ( 100 e r t ) f r = 100 e t ∂ ∂ r ( e r ) f r = 100 e t ( e r ) f r = 100 e r t Differentiate f with respect to t , we get ∂ f ∂ t = ∂ ∂ t ( 100 e r t ) f t = 100 e r ∂ ∂ t ( e t ) f t = 100 e r ( e t ) f t = 100 e r t Now, ∂ 2 f ∂ r 2 = f r r = ( f r ) r f r r = ∂ ∂ r ( 100 e r t ) f r r = 100 e t ∂ ∂ r ( e r ) f r r = 100 e t ( e r ) f r r = 100 e r t ∂ 2 f

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 8.4, Problem 36P

To determine

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

f=100ert

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Chapter 8.4, Problem 35P

Chapter 8.4, Problem 37P

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Chapter 8 Solutions

APPLIED CALCULUS (WILEY PLUS)

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Knowledge Booster

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. f = 100 e r t

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.

f=100ert

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Chapter 8 Solutions

To findall four second-order partial derivativesof below function and confirm that the mixed partials are equal. f = 100 e r t

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. f=100ert

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=100ert