Diffeomorphism: Unit Ball vs. Euclidean Space In my differential geometry class we are being asked to prove that the open unit ball 
$B^n$ = { $x$ $\in$ $\mathbb{R}$$^n$ such that |$x$| < $1$}  
is diffeomorphic to $\mathbb{R}$$^n$
I am having a hard time with this as I am brand new not only to differential geometry, but also topology.
I know that I need to construct a smooth, differentiable bijection between the two with a differentiable inverse, but beyond that, I am unsure of where to start. Some guidance in the right direction would be greatly appreciated. 

Or you can try $f(x)=x/\sqrt{1-|x|^2}$ for $x\in B^n$.
