Continuity of the derivative Df

[quasar987]

Homework Statement

I'm reading this at the moment: "Let f:R^n-->R^n be of class C^1 (that is, assume Df exists and is continuous)"

What does it mean?? If it means that for all x in R^n, the linear map Df(x):R^n-->R^n is continuous, then it's a triviality since all linear maps from R^n to R^m are continuous. So I am skeptical that this is what it means!

What other option is there? That map that send x in R^n to the point Df(x) in the space of linear map is a continuous map? I highly doubt that!

So what does it mean??

 

[morphism]

C^1 usually means continuous partials.

 

[quasar987]

Thanks for the tip!