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

[TommG]

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

 

[adjacent]

I think you will need chain rule too. Try doing it using chain rule + product rule

 

[HallsofIvy]

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

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

Second you are differentiating sin(x^2) with respect to \theta, not "\theta^2" so you need to multiply by the derivative of \theta^2 with respect to \theta.

 

[TommG]

thank you for your help I have figured it out