## University Calculus: Early Transcendentals (3rd Edition)

$ds/dt=5$
We have $s(\theta)=\cos\theta$ and $d\theta/dt=5$ According to the Chain Rule: $$\frac{ds}{dt}=\frac{ds}{d\theta}\frac{d\theta}{dt}=5\frac{ds}{d\theta}$$ $ds/d\theta$ refers to the derivative of $s(\theta)$, which is $s'(\theta)=-\sin\theta$. That means, $$\frac{ds}{dt}=-5\sin\theta$$ For $\theta=3\pi/2$: $$\frac{ds}{dt}=-5\sin\frac{3\pi}{2}=-5(-1)=5$$