Answer
$y'=-c\sin t+t^{2}\cos t+2t\sin t$
Work Step by Step
$y=c\cos t+t^{2}\sin t$ (Here, $c$ is a constant)
Differentiate each term:
$y'=(c\cos t)'+(t^{2}\sin t)'$
Use the product rule to find $(t^{2}\sin t)'$:
$y'=-c\sin t+(t^{2})(\sin t)'+(\sin t)(t^{2})'=...$
$...=-c\sin t+t^{2}\cos t+2t\sin t$
