Given a vectorfield X = (x,y,z)

1. Apr 3, 2005

carbis

Hello,

I hope a simple question for some of you:
Given a vectorfield X = (x,y,z), what is then for a general function f = f(x,y,z) the vectorfield X(f)?

2. Apr 3, 2005

mathwonk

Is it possible that X(f) is a function rather than a vector field?

I.e. the most obvious definition to me would be to let X(f) be the function whose value at a point p, is the derivative of f in the direction of the vector X(p).

I.e. a tangent vector at p is a differential operator that assigns a number to each differentiable function at that point. so a vector field, i.e. atangent vector at each point in an opern set, would assign to that function, a number for each point of the set.

this sounds like a function. doesn't it?