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Derivative of sin(x^2)cos(2x)

  1. Jun 13, 2014 #1
    Need to find derivative

    r = sin(θ2)cos(2θ)

    answer in book

    -2sin(θ2)sin(2θ)+2θcos(2θ)cos(θ2)


    My attempt

    tried using the product rule

    (sin(θ2))(-sin(2θ)) + cos(2θ)cos(θ2)

    I got stuck right here
     
  2. jcsd
  3. Jun 13, 2014 #2

    adjacent

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    Gold Member

    I think you will need chain rule too. Try doing it using chain rule + product rule
     
  4. Jun 13, 2014 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    adjacent it right- you need the chain rule.
    [tex]\frac{dy}{dx}= \frac{dy}{du}\frac{du}{dx}[/tex]

    First you are differentiating [itex]cos(2\theta)[/itex] with respect to [itex]\theta[/itex], not "[itex]2\theta[/itex]" so you need to multiply by the derivative of [itex]2\theta[/itex] with respect to [itex]\theta[/itex].

    Second you are differentiating [itex]sin(x^2)[/itex] with respect to [itex]\theta[/itex], not "[itex]\theta^2[/itex]" so you need to multiply by the derivative of [itex]\theta^2[/itex] with respect to [itex]\theta[/itex].
     
  5. Jun 13, 2014 #4
    thank you for your help I have figured it out
     
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