MTW defines the directional derivative of a vector along a parametrized
curve as:

lim(e-0) (v(e)-v(0))/e (page 209)

The problem is that the size of the resulting vector depends on your
parametrization of the curve. If you multiply your affine parameter with
a certain number, the size of your directional derivative vector also
changes. My question is: shouldn't there be some kind of correction for
the parametrization of the curve, like making the tangent vector of the
curve an unit vector? Mathworld
(http://mathworld.wolfram.com/DirectionalDerivative.html) says you have
to use an unit vector, but I couldn't find that in MTW.

Amantine