Question: defining and differentiating implicit functions

I am a newbie and this is the second post I am making. The previous follow-ups I received was very helpful and I appreciate it.

I am interested in using maple to derive derivatives of implicit functions. I have a function f(x,y) which I want to compute the gradients of it agaist r and theta. x and y are both functions of r and theta. I don't have a explicit form of f(x,y). My goal is to use this kind of operation to compute complicated higher order gradients of implicit functions so that I don't need to derive them by hand.

What is the best way to do this?

Thanks in advance for any help.

 

 

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