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Chain Rule for Vector Function

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data

    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.

    3. 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?
  2. jcsd
  3. Feb 8, 2012 #2


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    hi zoso335! :smile:

    ∇(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)​
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