$y=4\sin x\cos5x\sin6x$
$y'=4(\sin x)'\cos5x.\sin6x + 4\sin x(\cos5x)'\sin6x + 4\sin x\cos5x(\sin6x)'=4\cos x\cos5x\sin6x -20\sin x\sin5x\sin6x + 24\sin x\cos5x\cos6x$
$y=\cot\sqrt{x^2+1}$
$y'=\dfrac{-(\sqrt{x^2+1})'}{\sin^2\sqrt{x^2+1}}$
$=\dfrac{-(x^2+1)'}{2\sqrt{x^2+1}\sin^2\sqrt{x^2+1}}$
$=\dfrac{-x}{\sqrt{x^2+1}\sin^2\sqrt{x^2+1}}$