a. $y'=\frac{1}{2\sqrt{cot2x}}.(cot2x)'=\frac{1}{2\sqrt{cot2x}}.\frac{-1}{sin^22x}.(2x)'=-\frac{1}{\sqrt{cot2x}.sin^22x}$
b. $y'=cos(\sqrt{x^2+2}).(\sqrt{x^2+2})'=cos(\sqrt{x^2+2}).\frac{1}{2\sqrt{x^2+2}}.(x^2+2)'=cos(\sqrt{x^2+2}).\frac{1}{2\sqrt{x^2+2}}.2x=\frac{x.cos(\sqrt{x^2+2})}{\sqrt{x^2+2}}$
c. $y'=\frac{1}{2\sqrt{sinx+2x}}.(sinx+2x)'=\frac{cosx+2}{2\sqrt{sinx+2x}}$