What is a nonsingular derivative and how does it affect bijectivity?

[JamesTheBond]

What does a "nonsingular derivative" mean. It comes in the following context: "If f: R^2 --> R^2 is a function with a nonsingular derivative everywhere, is f bijective?"

 

[morphism]

It probably means it's invertible (i.e. it's a bijection).

 

[Data]

What does the derivative of a function $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$ look like? Do you know what it means for a matrix to be nonsingular (hint: see morphism's post!)?