- #1

ProPatto16

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## Homework Statement

If u=f(x,y) where x=e

^{s}cost and y=e

^{s}sint

show that d

^{2}u/dx

^{2}+d

^{2}u/dy

^{2}= e

^{-2s}[d

^{2}u/ds

^{2}+d

^{2}u/dt

^{2}

## The Attempt at a Solution

i have no idea!

question though, do the partial derivitives have to be solved and expanded then just show that one side equals the other or can it be proven by manipulating the terms as they are?

the only relevant chain rule is this one

du/ds=du/dx*dx/ds+du/dy*dy/ds and du/dt=du/dx*dx/dt+du/dy*dy/dt

this gives the first step of the partial derivitives to some of the question. how would i go about finding the second partial derivitive?

any help would be great!