Answer
$y' = 3x^{2}sinx\ cosx+x^{3}cos^{2}x-x^{3}sin^{2}x$
$y' = x^{2}sin^{2}x(3cotx + xcot^{2}x-x)$
Work Step by Step
$y = x^{3}sinx\ cosx$
$y' = (x^{3}sinx)cosx$
$y' = (3x^{2}sinx + x^{3}cosx)cosx - x^{3}sin^{2}x$
$y' = 3x^{2}sinx\ cosx+x^{3}cos^{2}x-x^{3}sin^{2}x$
$y' = x^{2}sin^{2}x(3cotx + xcot^{2}x-x)$