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

  • Thread starter TommG
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
adjacent
Gold Member
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I think you will need chain rule too. Try doing it using chain rule + product rule
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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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].
 
  • #4
28
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thank you for your help I have figured it out
 

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