I'm reading about the Gauss map. $\gamma(t)=r(u(t),v(t))$ is a curve along a surface and $n$ the map that sends the normal vectors in the curve to the sphere. I've seen the following manipulation:
$$n\circ \gamma (t) = n \circ r(u(t),v(t))$$
And hence:
$$(n \circ \gamma)'(0)=u' n_u + v' n_v$$
where $n_u= (n\circ r)_u$ and $n_v= (n\circ r)_v$.
Question: I understand that they are using the chain rule in there, but I am confused at what is going on in there. Could you expand a little bit more?