Explanation Given information: The equation is z = r 2 + s 2 + r s t , r 4 + s 4 + t 4 = 2 r 2 s 2 t 2 + 10 Calculation: Consider the equation. z = r 2 + s 2 + r s t …… (1) Consider the equation. r 4 + s 4 + t 4 = 2 r 2 s 2 t 2 + 10 …… (2) Differentiate equation (1). d z = 2 r d r + 2 s d s + r s d t + t r d s + t s d r ……. (3) Differentiate equation (2). 4 r 3 d r + 4 s 3 d s + 4 t 3 d t = 4 r 2 s 2 t d t + 4 t 2 r 2 r d r + 4 t 2 s 2 r d r ……. (4) Since, t is a constant. Thus, d t = 0 . The equation (3) becomes. d z = 2 r d r + 2 s d s + r s ( 0 ) + t r d s + t s d r d z = 2 r d r + 2 s d s + t r d s + t s d r d z = ( 2 r + t s ) d r + ( 2 s + t r ) d s ……. (5) The equation (4) becomes. 4 r 3 d r + 4 s 3 d s + 4 t 3 ( 0 ) = 4 r 2 s 2 t ( 0 ) + 4 t 2 r 2 s d s + 4 t 2 s 2 r d r 4 r 3 d r + 4 s 3 d s = 4 t 2 r 2 s d s + 4 t 2 s 2 r d r 4 r 3 − 4 t 2 s 2 r 4 t 2 r 2 s − 4 s 3 d r = d s ……

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Chapter 4.13, Problem 12MP

To determine

To find:The value of ∂z∂r .

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Chapter 4.13, Problem 11MP

Chapter 4.13, Problem 13MP

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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 value of ∂ z ∂ r .

Solution Summary: The author calculates the value of partial r, which is 13.

To find:The value of ∂z∂r .

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Chapter 4 Solutions