# Quick Question about Smooth Maps

Hello everyone, I just had a quick question I was hoping somebody could answer.

If $f: M \times N \rightarrow P$ is a smooth map, where $M,N$ and $P$ are smooth manifolds, then is it true for fixed $m$ that $f_m : N \rightarrow P$ is smooth, where $f_m (n) = f(m,n)$?

Any help would be appreciated.