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## Homework Statement

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}

## Homework Equations

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

The product rule

## 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.