Answer
Differentiate $f(\theta ) = \theta \cos \theta \sin \theta$
$f'(\theta)= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$
Work Step by Step
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
$= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$
