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High order derivatives

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data

    if f(x)=cos2x, how do we know that f^50 = f^2 ??

    In the solution it states that because 50 = (12)(4) + 2, then f^50 = f^2.

    What the??
     
  2. jcsd
  3. Mar 17, 2009 #2

    Mark44

    Staff: Mentor

    We don't know that f(50) = f(2) for the reason that it isn't true. If the function were f(x) = cos(x), it would be true, though, and this is easy enough to verify by taking a few derivatives and noticing the cyclical nature of these derivatives.
     
  4. Mar 17, 2009 #3
    Okay, well how do they know that f^2 = f^50 for cosx simply by going 50 = (4)(12) + 2
     
  5. Mar 17, 2009 #4
    Because it repeats every four times
    cosx
    -sinx
    -cosx
    sinx
    cosx
     
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