(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

z=f(x,y)

x=e^{s}cos(t)

y=e^{s}sin(t)

show d^{2}z/dx^{2}+d^{2}z/dy^{2}= e^{-2s}[d^{2}z/ds^{2}+ d^{2}/dt^{2}

2. Relevant equations

dz/dt=dz/dz(dx/dt)+(dz/dy)dy/dr

The product rule

3. The attempt at a solution

I found d^{2}x/dt^{2}=2e^{2s}sin(t)cos(t)d^{2}z/dydx + e^{2s}cos^{2}(t)d^{z}/dy^{2}

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 d^{2}z/dydx term.

Thank your for your help.

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# Proof Involving Partial Derivatives Chain Rule

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