Explanation Given information: The given expressions are w = e − r 2 − s 2 , r = u v and s = u + 2 v . Calculation: w = e − r 2 − s 2 ............ (1) r = u v ............(2) s = u + 2 v ............ (2) Differentiate the equation (1) d w = e − r 2 − s 2 ( − 2 r d r − 2 s d s ) d w = − 2 e − r 2 − s 2 ( r d r + s d s ) d w = − 2 w ( r d r + s d s ) d w = − 2 w ( r u d v + r v d u + s

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 4P

To determine

To find:The dwdu , dwdv .

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Chapter 4.7, Problem 3P

Chapter 4.7, Problem 5P

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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 d w d u , d w d v .

Solution Summary: The author explains that the given expressions are w=e-r2

To find:The dwdu , dwdv .

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Chapter 4 Solutions