Simple Question: Derivative of a path

I have a path V[t_]:={3t^2,2,6t}, and I define F[t_]:=V[t]/Norm[V[t]]. I simply want the derivative of F, which is a 3-vector function of the variable t. Somehow I did not manage to find any (simple?) way to calculate it.. Ideas?

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You might want to use V[t]/Sqrt[V[t].V[t]] instead. –  Ｊ. Ｍ. Apr 19 '13 at 8:35
Alternatively, you have to use Assuming or the Assumptions when you will simplify the derivative of the function F –  Spawn1701D Apr 19 '13 at 8:43
Thanks... I also didn't notice in my attempts.., that Mathematica was still complaining about an ancient error, hidden behind my window... –  Dror Apr 19 '13 at 8:48
@Dror And you are sure you want this instead of the normalized derivative of v, which is the direction vector along the path? –  halirutan Apr 19 '13 at 9:28
@halirutan , thanks for the nice tip. Though, In my case (which, regretfully, I did not specify), V is actually the derivative of my original path, and I wanted to find It's normal. –  Dror Apr 19 '13 at 10:25
v[t_] := {3 t^2, 2, 6 t};

Yes, that works. Somehow It didn't work when using Norm[]. Thanks! (In my next questions, all will be specified! :) ) –  Dror Apr 19 '13 at 10:26