# Homework Help: Derivative of sin(x^2)cos(2x)

1. Jun 13, 2014

### TommG

Need to find derivative

r = sin(θ2)cos(2θ)

-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. Jun 13, 2014

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

3. Jun 13, 2014

### 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 $\theta$.

4. Jun 13, 2014

### TommG

thank you for your help I have figured it out