One knows that $$f(x,y)=\frac{x^\alpha y^\beta}{x^2+y^2}$$ is continuous iff $\alpha+\beta>2$.
Is there any condition of $\alpha$ and $\beta$ so that the previous function is differentiable?
One knows that $$f(x,y)=\frac{x^\alpha y^\beta}{x^2+y^2}$$ is continuous iff $\alpha+\beta>2$.
Is there any condition of $\alpha$ and $\beta$ so that the previous function is differentiable?