Hi, I need help on the following:

Let $\displaystyle f : \mathbb{R}^2 \to \mathbb{R}^2 $ be defined by $\displaystyle f(x,y) = (y, x^2) $. Prove that it is differentiable at $\displaystyle (0,0) $.

I know the partial derivatives exist at $\displaystyle (0,0) $.

Thanks