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A simple problem pertaining to divergence

  1. Jul 31, 2016 #1
    1. The problem statement, all variables and given/known data

    The problem states that it is required to prove that ∇f(r)=f'(r)R/r where r is the vector field
    2. Relevant equations
    ∇=(∂/∂x)i + (∂/∂y)j + (∂/∂z)k
    R= xi + yj +zk
    r = √(x^2+y^2+z^2)

    3. The attempt at a solution

    The trouble that I am having with this problem is the inability to truly comprehend what f(r) truly means⋅ Is f(r) dependent on the vector field R???
     
  2. jcsd
  3. Jul 31, 2016 #2
     
  4. Jul 31, 2016 #3
    Is f(r) = f(x)i + f(y)j +f(z)k what being meant in the above stated problem???
     
  5. Jul 31, 2016 #4

    Ray Vickson

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    Homework Helper

    ##f(r) = f\left(\sqrt{x^2+y^2+z^2}\right)##, because ##r## means ##\sqrt{x^2+y^2+z^2}##, as you, yourself, have written.
     
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