a. Explanation Given: z = x + y 2 Where, x = u + v , y = u − v Calculation: To find the partial derivatives ∂ z ∂ u , ∂ z ∂ v , where z = x + y 2 Where, x = u + v , y = u − v , first lets express z in terms of u and v , as z = x + y 2 = ( u + v ) + ( u − v ) 2 = u + v + u 2 + v 2 − 2 u v Now, to find ∂ z ∂ u differentiate above with respect to u treating v as constant, as ∂ z ∂ u = ∂ ∂ u ( u + v + u 2 + v 2 − 2 u v ) = b. To determine To find the partial derivatives ∂ z ∂ u , ∂ z ∂ v , where z = x + y 2 Where, x = u + v , y = u − v

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ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11.5, Problem 8PS

To determine

To find the partial derivatives ∂z∂u,∂z∂v , where

z=x+y2

Where, x=u+v,y=u−v

To determine

To find the partial derivatives ∂z∂u,∂z∂v , where

z=x+y2

Where, x=u+v,y=u−v

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Chapter 11.5, Problem 7PS

Chapter 11.5, Problem 9PS

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To find the partial derivatives ∂ z ∂ u , ∂ z ∂ v , where z = x + y 2 Where, x = u + v , y = u − v

Solution Summary: The author explains how to find the partial derivatives of partial z, v, and u.

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To find the partial derivatives ∂z∂u,∂z∂v , where z=x+y2 Where, x=u+v,y=u−v

To find the partial derivatives ∂z∂u,∂z∂v , where z=x+y2 Where, x=u+v,y=u−v

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Chapter 11 Solutions

To find the partial derivatives ∂z∂u,∂z∂v , where

z=x+y2

Where, x=u+v,y=u−v

To find the partial derivatives ∂z∂u,∂z∂v , where

z=x+y2

Where, x=u+v,y=u−v