I was studying some notes of classes and I am stucked at the following proposition:
Let $S_1,S_2,S_3$ be orientated surfaces. If $S_1\stackrel{f}{\to}S_2\stackrel{g}{\to}S_3$ are local diffeomorphisms, so $g\circ f$ preservs orientation.
As a sketch of proof, the professor wrote:
$d(g\circ f)=dg_{f(p)}\circ df_p.$
Well, I could not understand this. For instance, if $f$ preservs orientation and $g$ invertes orientation, so I was thoughting why $g\circ f$ preservs orientation?
Many thanks in advance.