Partial Derivatives Challenge Question

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?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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