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Simplifying wrong or completely wrong?

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data
    Find dy/dx.
    [itex]y=sin^{2}(3x-2)[/itex]


    2. Relevant equations



    3. The attempt at a solution
    Using the chain rule,
    [itex]y=sin^{2}u[/itex]
    [itex]y'=2sinucosu[/itex]
    [itex]u=3x-2[/itex]
    [itex]u'=3[/itex]

    [itex]\frac{dy}{dx}=6sin(3x-2)cos(3x-2)[/itex]

    Answer is:
    [itex]3sin(6x-4)[/itex]


    What am I missing here ?
     
  2. jcsd
  3. Nov 16, 2011 #2

    Mark44

    Staff: Mentor

    Your answer is correct, and so is the other answer you show. They are using the identity sin(2A) = 2sin(A)cos(A). In your problem A = 3x - 2.
     
  4. Nov 16, 2011 #3

    lurflurf

    User Avatar
    Homework Helper

    The identity

    sin2(u)=(1/2)[1-cos(2x)]
    so
    [sin2(u)]'=[(1/2)[1-cos(2x)]]'=sin(2u)u'
     
  5. Nov 16, 2011 #4
    Ah, I remember that now, now I'll remember that identity, thank you.
     
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