#### Answer

The Derivative is:
$\frac{dr}{d\theta}=\theta\cos\theta$

#### Work Step by Step

$r=\theta\sin\theta+\cos\theta$
Applying Derivative rules:
$y'=f'(x)+g'(x)$ $and$ $f'(x)=h'(x)\cdot v(x)+h(x)\cdot v'(x)$
$\frac{dr}{d\theta}=\frac{d}{d\theta}(\theta\sin\theta)+\frac{d}{d\theta}(\cos\theta)$
$\frac{dr}{d\theta}=(\theta^{1-1}(\sin\theta)+\theta(\cos\theta))+(-\sin\theta)$
$\frac{dr}{d\theta}=\sin\theta+\theta\cos\theta-\sin\theta$
$\frac{dr}{d\theta}=\theta\cos\theta$