Explanation Given information: The equation is w = f ( x , x 2 + y 2 , 2 x y ) . Calculation: Consider the function. w = f ( x , x 2 + y 2 , 2 x y ) ........... (1) Consider the equation. s = x 2 + y 2 ........... (2) Consider the equation. t = 2 x y ........... (3) Differentiate equation (2). d s = 2 x d x + 2 y d y Differentiate equation (2). d t = 2 y d x + 2 x d y Differentiate equation (1). d w = ∂ f ∂ x d x + ∂ f ∂ s d s + ∂ f ∂ t d t = ∂ f ∂ x d x + ∂ f ∂ s ( 2 x d x + 2 y d y ) + ∂ f ∂ t ( 2 y d x + 2 x d y ) = ( ∂ f ∂ x + 2 x ∂ f ∂ s + 2 y ∂ f ∂ t ) d x + ( 2 y ∂ f ∂ s + 2 x ∂ f ∂ t ) d y Since, the constant is y

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Question

Chapter 4.13, Problem 15MP

To determine

To find:The value of ( ∂w ∂x)y in terms of f .

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Chapter 4.13, Problem 14MP

Chapter 4.13, Problem 16MP

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Chapter 4 Solutions

Mathematical Methods in the Physical Sciences

Ch. 4.1 - If u=x2/x2+y2, find u/x,u/y.Ch. 4.1 - Prob. 2P Ch. 4.1 - If z=lnu2+v2+w2, find z/u,z/v,z/w.Ch. 4.1 - For w=x3y32xy+6, find 2w/ax2 and 2w/ay2 at the...Ch. 4.1 - For w=8x4+y42xy2, find 2w/x2 and 2w/y2 at the...Ch. 4.1 - For u=excosy, (a) verify that 2u/xy=2u/yx; (b)...Ch. 4.1 - Prob. 7P Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...

Knowledge Booster

The value of ( ∂ w ∂ x ) y in terms of f .

Solution Summary: The author calculates the value of (partial wpdx)_y in terms of f.

To find:The value of ( ∂w ∂x)y in terms of f .

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Chapter 4 Solutions