Let $f: \mathbb{C}^2\rightarrow\mathbb{C}^2$ be the map $(z,w)\mapsto(z^3-w^3,zw)$. In which points $(z,w)$ is f a local diffeomorphism?
I struggle to solve this problem. From what I know a diffeomorphism is a bijective map whose inverse is differentiable (?) Now what makes a local diffeomorphism and how could I use that to solve this problem? Thanks!