Hi, I have a question.

If I have a path that is parameterized by a variable 's',
the derivative of the coordinates with respect to 's' is a
contravariant tensor, yes? I have a textbook that uses
the covariant derivative of this tensor (to derive the
absolute derivative). The first term of the covariant derivative
is not sensible to me (not the term involving the
Christoffel symbol). What does it mean to take the
partial derivative of a function of 's' with respect to
one of the coordinates?

-Mike