Question

an object travels along a straight line. the function $s(t) = t^{4}\cos t$ gives the objects position, in miles, at time $t$ hours.
write a function that gives the objects velocity $v(t)$ in miles per hour.
$v(t) = $

Explanation:

Step1: Recall product rule for derivatives

For $f(t)=u(t)v(t)$, $f'(t)=u'(t)v(t)+u(t)v'(t)$

Step2: Define $u(t)$ and $v(t)$

Let $u(t)=t^4$, $v(t)=\cos t$

Step3: Compute $u'(t)$ and $v'(t)$

$u'(t)=4t^3$, $v'(t)=-\sin t$

Step4: Apply product rule

$v(t)=4t^3\cos t + t^4(-\sin t)$

Answer:

$v(t)=4t^3\cos t - t^4\sin t$