Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 2r cos(0) and y = 2r sin(8), find the following. az (a) ar az (2 cos (0) 2 sin(0)) az ar ax (b) az az az -2r sin (0)) + z( 2rcos(0)) a2z (c) ar ae ( 2 cos(0) -2 sin (0) Day ax ar de ay2 ax2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Assume that all the given functions have continuous second-order partial derivatives. If z = f(xy), where 

x = 2r cos(?)

 and 

y = 2r sin(?),

 find the following.

 

Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 2r cos(0) and y = 2r sin(6), find the following.
az
(a)
ar
az
ax
dz
az
( 2 cos (0)) + ( 2 sin(0))
ar
az
(b)
az
az
-2r sin (0)
ax
2r cos(0)D
a2z
(c)
ar ae
z + ( -2 sin(0) )*
a2z
a2z
a2z
a2z
( 2 cos(e)
=
ar de
ду
ax2
ay əx
Transcribed Image Text:Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 2r cos(0) and y = 2r sin(6), find the following. az (a) ar az ax dz az ( 2 cos (0)) + ( 2 sin(0)) ar az (b) az az -2r sin (0) ax 2r cos(0)D a2z (c) ar ae z + ( -2 sin(0) )* a2z a2z a2z a2z ( 2 cos(e) = ar de ду ax2 ay əx
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