## Calculus 8th Edition

Differentiate $f(\theta ) = \theta \cos \theta \sin \theta$ $f'(\theta)= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$
Use the product rule and trig rules. $f'(\theta) = \cos \theta \sin \theta - \theta \sin ^2 \theta + \theta \cos ^2\theta$ $=\cos \theta \sin \theta +\theta(\cos ^2 \theta - \sin ^2 \theta)$ Use trig identities to simplify $= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$