eader may
take it as an object lesson in differential translation.

| 2.2.  Submanifolds, Immersions, Submersions (cont.)
|
| If U, V are open in Banach spaces, then to every morphism f
| of class C^p (p &gt;= 1) we can associate its derivative Df(x).
| If now f : X -&gt; Y is a morphism of one manifold into another,
| and x a point of X, then by means of charts we can interpret
| the derivative of f on each chart at x as a mapping:
|
| df(x)  =  T_x f  :  T_x (X)  -&gt;  T_f(x) (Y).
|
| Indeed, this map T_