## Calculus: Early Transcendentals 8th Edition

$g'(\theta)=-2\sin\theta\cos\theta$ or $g'(\theta)=-\sin2\theta$
$g(\theta)=\cos^{2}\theta$ Differentiate using the chain rule: $g'(\theta)=2\cos\theta(\cos\theta)'=2(\cos\theta)(-\sin\theta)=...$ $...=-2\sin\theta\cos\theta$ Also you can use the identity $2\sin\theta\cos\theta=\sin(2\theta)$ to present the answer like this: $g'(\theta)=-\sin2\theta$