diffeomorphism in $\mathbb R^n$

Question

We have $$f:(0,\infty)\times (0,\infty)\rightarrow \mathbb{R}^{2}$$ $$f(x,y)=(x^{2} - y^2,xy)$$ How can I show this function is a diffeomorphism of class $C^{\infty}$ of $(0,\infty)\times (0,\infty)$ in a open set in $\mathbb R^{2}$?