1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Gradient operation proof

  1. Nov 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the operation of taking the gradient of a function has the given property. Assume u and v are differentiable functions of x and y and that a and b are constants.

    Operation: (∇(u))n = n*un-1*∇u

    2. Relevant equations

    The gradient vector of f is <∂f/∂x,∂f/∂y>, where f is a function of x and y (in other words f(x,y)).

    3. The attempt at a solution

    I tried proof by induction, but I have a lot of gaps.

    Base, n=1: ∇u = n*u0∇u. But what is u0 if u is a function?

    Assume n = k: ∇uk = n*uk-1∇u

    For k=k+1, ∇uk+1 = n*uk∇u.

    Isn't proof by induction for sums though? I can't seem to identify the sum here.

    Any help would be greatly appreciated!
  2. jcsd
  3. Nov 25, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    You have got to mean ## \nabla (u^n)=n u^{n-1} \nabla u ##, ## (\nabla(u))^n ## doesn't mean anything. Just use the chain rule for partial derivatives.
  4. Dec 1, 2012 #3
    Oh I see. Thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook