Chain Rule for Vector Function

[zoso335]

Homework Statement

I'm trying to figure out how to take grad(f(x(t)) where x(t) is a vector. Since it's part of a physics problem, it's assumed x(t) is in 3-dimensional space.

The Attempt at a Solution

My guess is that grad(f(x(t)) = ((∂f/∂x)(∂x/∂x),(∂f/∂x)(∂x/∂y),(∂f/∂x)(∂x/∂z)) but I really am not sure about this. Can anyone point me in the right direction?

 

[tiny-tim]

hi zoso335!

∇(f(x,y,z)) = (∂/∂x(f(x,y,z)) , ∂/∂y(f(x,y,z)) , ∂/∂z(f(x,y,z)))

= (∂f/∂x , ∂f/∂y , ∂f/∂z)​