Hi there, I have this exercise, I'd like to know what you think, if I did this right:

If , with . Determine if its possible the dF over a point adequately chosen.

So I choose which satisfies the system

Then I've verified that satisfies the implicit function theorem, both functions are polynomials of class y

then

Then I consider:

And I set:

From where I get:

Analogous procedure for the derivatives with respect to y, and:

Is this right?

Bye.