Question

Find the derivative: s=t^4 cos t - 7t sin t - 7 cos t

Answer 1

\[s(t)=t^4\cos t-7t\sin t-7\cos t\\
s'(t)=\left(\frac{d}{dt}\left[t^4\right]\cos t+t^4\frac{d}{dt}\left[\cos t\right]\right)-7\left(\frac{d}{dt}\left[t\right]\sin t+t\frac{d}{dt}\left[\sin t\right]\right)-7\frac{d}{dt}\left[\cos t\right]\]

Answer 2

would it be the same as a ds/dt answer?

Answer 3

http://www.wolframalpha.com/input/?i=derivative+of+t%5E4cost+-+7tsint+-+7cost

Answer 4

@michael.tolin ,
\[\frac{ds}{dt}=s'(t),\text{ so yes.}\]