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Proof Involving Partial Derivatives Chain Rule 
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#1
Jan2510, 10:32 PM

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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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