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Ok, so I have f(x,y)=(p(x)+q(y))/(x^2+y^2) where (x,y)NOT=0 and f(0,0)=0. the basic idea of the function is that the numerator contains 2 polynomials>2nd order. and the denominator has a Xsquared+ysquared. I have to prove that if f(x,y) is differentiable at (0,0) then its partial derivatives fx and fy are both continous. I need something rigorous i was thinking of doing something where the tangent h(x,y) approximates f(x,y) as dx, dy go to 0. and then from there.... IDK i need all help i can get. Thank you in advance