The Connection (vector_bundle) article of Wikipedia mentions about Ehresmann connection that a smooth map $s:M\to E$ ($E$ is any vector bundle over $M$) has a differential $ds:TM\to TE$, this means there is tangent spaces on the vector bundle $E$.
What is the condition that tangent space can be defined on fiber bundle? Article about fiber bundle and vector bundle doesn't mention that the bundle is also a smooth manifold.
IMO if both the base space and the fiber space are smooth manifolds then the fiber bundle is also a smooth manifold whose tangent space at any point has a dimmension of the sum of the dimmensions of the both spaces? In the above special case, the fiber of $E$ is $R^n$ which is a smooth manifold.
Is that right?