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Trigonometric derivative: power rule + product rule

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Derive the following:

    y = (cosxsin2x)-2


    2. The attempt at a solution

    Basically I saw this as a power rule with two products in the middle.

    So y = -2 (cos2cos2x-sinxsin2x)-1

    But the correct answer is completely different, it's:

    4(3sin2x - 1) all over
    cos2xsin32x

    Could someone please go through the steps to get to the correct solution? Thanks in advance!
     
  2. jcsd
  3. May 2, 2010 #2
    [tex] y = (cos{x}sin{2x})^{-2} [/tex]

    [tex] \frac{dy}{dx} = -2(\cos{x}\sin{2x})^{-3}[\underbrace{\frac{d}{dx}(\cos{x}\sin{2x})}_{use\: product \:rule}] [/tex]
     
    Last edited: May 2, 2010
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