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Math Help - Double Check Trig Derivative Question

  1. #1
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    Feb 2008
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    Double Check Trig Derivative Question

    The function is: f(x)=2*cos^3x+cos^4x

    My derivative is:
    f'(x)=-sin(2x)cos(x)(3+2*cos(x))

    The back gives a totally different answer... I want to confirm mine.
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  2. #2
    Member
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    Dec 2008
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    Auckland, New Zealand
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    Differentiate 2\cos^3{x} and you get -6\cos^2{x}\sin{x} = -3\sin{2x}\cos{x}

    Differentiate \cos^4{x} and you get -4\cos^3{x}\sin{x} = -2\sin{2x}\cos^2{x}

    Adding and factorising....

    f'(x) = -3\sin{2x}\cos{x} - 2\sin{2x}\cos^2{x} = -\sin{2x}\cos{x}\,(3+2\cos{x})
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