Partial Derivatives Challenge Question

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kingwinner
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http://www.geocities.com/asdfasdf23135/advcal9.JPG

I find this question to be extremely challenging...

The best I can think of is z=f(x,y)=ln(theta), would this work?

Can someone teach me how to define S=domain of f? This problem is giving me bad headaches.

It would be nice if someone can guide me through the solution.

Thanks a million!
 
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I find it difficult. Anyone willing to take up this challenge?