$10) y' = \cot \dfrac{x}{3} - \dfrac{x}{3} .\dfrac{1}{\sin^2 \dfrac{x}{3}}$
$9) y'= 3\tan^2 x .\dfrac{1}{\cos^2 x}+\dfrac{2}{\sin^2 2x}$
$8) y'=\dfrac{\cos \dfrac{x}{\pi}}{2\pi .\sqrt{-1+\sin \dfrac{x}{\pi}}}$
$7) y' =\dfrac{2\sin x \cos x (1+\tan 2x) -\sin^2 x .\dfrac{2}{\cos^2 2x}}{(1+\tan 2x)^2}=\dfrac{\sin 2x (1+\tan 2x) -\sin^2 x(1+\tan^2 2x)}{(1+\tan 2x)^2}$