Suppose Dvf (a) exists. Prove that D-vf (a) exists and calculate in terms of the former.
2007-09-24 14:35:53 · 2 answers · asked by Dr H 2 in Science & Mathematics ➔ Mathematics
oh sorry Dvf(a) and D-vf(a) are the directional derivitives of f at a, in the direction of v, i think the D-vf(a) is the same but with direction -v) sorry about that hopefully that clairfyies the question
2007-09-24 15:20:49 · update #1
I assume v is a unit vector. Since Dvf(a) exists, we have
Dvf(a) = (del)f(a)*v, where "del"is the vector differential operator and * is the dot product. It follows that D-vf(a) =
(del)f(a)*(-v) = -(del)f(a)*v = -Dvf(a).
2007-09-27 09:33:23 · answer #1 · answered by Tony 7 · 0⤊ 0⤋
Forgive me if I'm being dumb and missing something obvious (it's the early hours of the morning here in Blighty), but what does your notation mean?
What do Dvf(a) and D-vf(a) represent?
2007-09-24 14:49:06 · answer #2 · answered by SV 5 · 0⤊ 0⤋