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Proof Involving Partial Derivatives Chain Rule

by runningeagle
Tags: chain, derivatives, involving, partial, proof, rule
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runningeagle
#1
Jan25-10, 10:32 PM
P: 1
1. The problem statement, all variables and given/known data
z=f(x,y)

x=escos(t)

y=essin(t)

show d2z/dx2+d2z/dy2 = e-2s[d2z/ds2+ d2/dt2


2. Relevant equations
dz/dt=dz/dz(dx/dt)+(dz/dy)dy/dr

The product rule


3. The attempt at a solution

I found d2x/dt2=2e2ssin(t)cos(t)d2z/dydx + e2scos2(t)dz/dy2

But, now I'm lost. It doesn't seem to be going anywhere. I don't know where I am going to get rid of the d2z/dydx term.

Thank your for your help.
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