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

See similar textbooks

Question

Chapter 4.13, Problem 12MP

To determine

To find:The value of ∂z∂r .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.13, Problem 11MP

Chapter 4.13, Problem 13MP

Students have asked these similar questions

3. A room has a large circular table with ten seats, numbered 1 to 10, such that to the right of seat number i is seat number i + 1 for all i ∈ {1, . . . , 9} and to the right of seat 10 is seat 1. We want to assign seats to 10 people, 6 of them only speak Slovene, 1 of them only speaks English, and the remaining 3 speak both Slovene and English, by giving out numbered place cards. In how many ways can we do that so that everyone sits next to at least one person who speaks a common language?

charity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisure

Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.

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 ∂ z ∂ r .

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

To find:The value of ∂z∂r .

Want to see the full answer?

Chapter 4 Solutions