$y=4\sin x.\cos 5x.\sin6x$
$y'=(4\sin x)'.(\cos5x.\sin6x)+4\sin x(\cos5x.\sin6x)'$
$=4\cos x.\cos5x.\sin6x + 4\sin x.[(\cos5x)'\sin6x+ \cos5x.(\sin6x)']$
$=4\cos x.\cos 5x.\sin6x + 4\sin x(-5\sin 5x.\sin6x +\cos5x.6\cos 6x)$
$=4\cos x.\cos 5x.\sin6x -20\sin x.\sin5x.\sin6x+24\sin x\cos 5x.\cos6x$
