x f is the unique linear map having the following property.
| If (U, q) is a chart at x and (V, r) is a chart at f(x) such that f(U) c V
| and ^v^ is a tangent vector at x represented by v in the chart (U, q),
| then:
|
| T_x f(^v^)
|
| is the tangent vector at f(x) represented by (Df_V,U (x))v.
| The representation of T_x f on the spaces of charts can be
| given in the form of a diagram:
|
|       T_x (X)  o--------&gt;o  E
|                |         |
|         T_x f  |         |  f'_V,U (x)
|            