Explanation Given that u 2 + v 2 = x 3 − y 3 + 4 u 2 − v 2 = x 2 y 2 + 1 Consider the function f ( x , y , u , v ) = 0 The term ( ∂ u ∂ x ) y denote the partial derivative of the function u ( x , y ) with respect to x keeping y fixed So, firstly assume that the given function as f ( x , y , u , v ) = 0 ( ∂ u ∂ x ) v = [ x y 2 ] ( u ) = ( x 3 − y 3 − x 2 y 2 + 3 ) y 2 + 1 2 Similarly, ( ∂ u ∂ x ) y = [ x y 2 ] ( u ) = u 2 − v 2 + 1 x 2 Similarly, ( ∂ x ∂ u ) v = ( x 3 − y 3 − x 2 y 2 + 3 ) x 2 2

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 4.7, Problem 20P

To determine

To find:The partial differential of each equation ( ∂u ∂x)y , ( ∂u ∂x)v , ( ∂x ∂u)y , ( ∂x ∂u)v .

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Chapter 4.7, Problem 19P

Chapter 4.7, Problem 21P

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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...

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The partial differential of each equation ( ∂ u ∂ x ) y , ( ∂ u ∂ x ) v , ( ∂ x ∂ u ) y , ( ∂ x ∂ u ) v .

Solution Summary: The author explains how to find the partial differential of each equation (partial x)_y.

To find:The partial differential of each equation ( ∂u ∂x)y , ( ∂u ∂x)v , ( ∂x ∂u)y , ( ∂x ∂u)v .

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Chapter 4 Solutions