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