Deduce from that in the definition of directional derivative, , the straight line can be replaced by any curve with initial velocity , that is, such that and
Not quite sure how to proceed. Any help would be appreciated.
Deduce from that in the definition of directional derivative, , the straight line can be replaced by any curve with initial velocity , that is, such that and
Not quite sure how to proceed. Any help would be appreciated.
Try replacing with and see what you get. In the standard directional derivative definition, you're traveling from p along a straight line in the direction of v, and taking the limit as t goes to zero. They're saying that you could travel t units along the path alpha, and take the same t->0 limit, and get the same answer, provided alpha has the right properties.