1.
$y'=(x^6)'(x-2)+x^6(x-2)'$
$=6x^5(x-2)+x^6$
$=7x^6-12x^5$
2.
$y'=\dfrac{(\sin x+\cos x)'x-x'(\sin x+\cos x)}{x^2}$
$=\dfrac{(\cos x-\sin x)x-(\sin x+\cos x)}{x^2}$
$=\dfrac{x\cos x-x\sin x-\sin x-\cos x}{x^2}$
3.
$y'=\dfrac{(\sqrt{2x-1})'x-\sqrt{2x-1}}{x^2}$
$=\dfrac{\dfrac{1}{\sqrt{2x-1}}.x-\sqrt{2x-1}}{x^2}$
$=\dfrac{x-(2x-1)}{x^2(\sqrt{2x-1})}$
$=\dfrac{-x+1}{x^2\sqrt{2x-1}}$
4.
$y'=2\sin\Big(2x-\dfrac{\pi}{4}\Big).\Big(\sin\Big(2x-\dfrac{\pi}{4}\Big)\Big)'$
$=2\sin\Big(2x-\dfrac{\pi}{4}\Big).2\cos\Big(2x-\dfrac{\pi}{4}\Big)$
$=2\sin\Big(4x-\dfrac{\pi}{2}\Big)$
$=-2\cos4x$
