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Differentiation Rules of Sinusoidal Functions

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data
    f(x) = cos2x - sin2x


    3. The attempt at a solution
    f'(x) = (2cosx)(-sinx) - (2sinx)(cosx)
    f'(x) = -2cosxsinx - 2sinxcosx

    This is what I think the answer should be, but the back of the book says otherwise. I need help identifying what I did wrong.
     
  2. jcsd
  3. Mar 14, 2012 #2

    SammyS

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    ... And what would that otherwise be?

    Perhaps something involving sine and/or cosine of 2x ?

    ... or just a simplified version of what you have?

    -2ab - 2ba = -4ab ?
     
  4. Mar 14, 2012 #3
    It says the answer should be f'(x) = -2sin2x.
     
  5. Mar 14, 2012 #4
    Recall this identity: [itex]2sin(x)cos(x) = sin(2x)[/itex]
     
  6. Mar 14, 2012 #5
    Oh wow forgot entirely about that. These kinds of mistakes will be the end of me. :redface: Thanks for the help.
     
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