(2) Supose f(x, Y, z) = g(p), where p = Vx? + y? + 2² and g is a function of one variable. Prove that 2 faæ (x, Y, z) + fyy(x, Y, z) + fzz(x, Y, z) = g" (p) + -g'(e) as long as (x, y, z) # (0,0,0). Note that g'(p) dg do %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Quiz #6 q#2

(2) Supose f(x, Y, z) = g(p), where p = Vx2 + y² + 22 and g is a function of one variable. Prove
that
2
fwx (x, y, z) + fyy(x, Y, z) + fzz(x, y, z) = g" (p) +-g'(p)
ZZ
as long as (x, Y, z) # (0,0, 0). Note that gʻ(p)
dg
dp
Transcribed Image Text:(2) Supose f(x, Y, z) = g(p), where p = Vx2 + y² + 22 and g is a function of one variable. Prove that 2 fwx (x, y, z) + fyy(x, Y, z) + fzz(x, y, z) = g" (p) +-g'(p) ZZ as long as (x, Y, z) # (0,0, 0). Note that gʻ(p) dg dp
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