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: Proof of Power Rule for 2 variables

  1. Mar 4, 2009 #1
    1. The problem statement, all variables and given/known data

    u^n (x,y)=nu^(n-1) (x,y) u' (x,y)

    2. Relevant equations



    3. The attempt at a solution
    can i set f (x,y)=u^n (x,y)
    lnf =lnu^n
    lnf=nlnU
    f'/f=n/U
    f'=fn/U -(U(^n) )(n/U)
    after that i dont know how to continue and is there a better way to prove it
     
  2. jcsd
  3. Mar 4, 2009 #2

    HallsofIvy

    User Avatar
    Science Advisor

    What do you mean by "u'(x,y)"? The gradient? The differential? "u' " is not defined for a function of two variables. If you mean the gradient, which is what I would think of as "the" derivative for a function of several variables, then yes, [itex]\nabla u^n(x,y)= nu^{n-1}\nabla u[/itex]. That follows from the chain rule.

     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook