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Can I pull a time derivative outside of a curl?

  1. May 6, 2015 #1
    1. The problem statement, all variables and given/known data
    For the equation ∇ x E = -∂B/∂t I took the curl of both sides to get

    ∇ x (∇ x E) = ∇ x -∂B/∂t

    I feel like it'd be very wrong to pull out the time derivative. Am I correct?
     
  2. jcsd
  3. May 6, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    No, you can pull out the time derivative.
     
  4. May 7, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Yes, this is just the property of interchangeability of partial derivatives: ##\partial / \partial t \; \partial / \partial \psi f(\psi,t) = \partial /\partial \psi \; \partial / \partial t f(\psi,t)##.
     
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