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Multivariable Calculus Question involving gradients

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that [tex]\nabla[/tex](r^n)=nr^(n-2)r if n is a position integer.
    (hint:use [tex]\nabla[/tex](fg)=f[tex]\nabla[/tex]g+g[tex]\nabla[/tex]f)
    2. Relevant equations

    let r(x,y,z) = xi+yJ+zK be the position vector and let r(x,y,z)= |r(x,y,z)|

    3. The attempt at a solution

    I tried separating [tex]\nabla[/tex](r^n) to [tex]\nabla[/tex](r^(n-1)*r)

    but I can't figure it out.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 24, 2010 #2
    I think you may try mathematical induction
     
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