Answer
$f'(\theta)=\cos{\theta}-(\theta+1)\sin{\theta}.$
Work Step by Step
Product Rule $f'(\theta)=((u(\theta)(v(\theta))’=u’(\theta)v(\theta)+u(\theta)v’(\theta))$.
$u(\theta)=(\theta+1) ;u’(\theta)=1 $
$v(\theta)=\cos(\theta) ;v’(\theta)=-\sin(\theta) $
$f'(\theta)=(1)(\cos(\theta))+(-\sin(\theta))(\theta+1)$
$=\cos{\theta}-(\theta+1)\sin{\theta}$.
