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I have been working on determining which partial derivative exists for the surface z=y. i.e. ( partial of f in respect to x, partial of f in respect to y, partial of f in resprct to z). The function f= x^2 -y-z. I think the only ones that exist would be the partial in respect to y and the partial in respect to z since the surface is z=y. Am I on the right track?