$
\eqalign{
& y = \sqrt {2x} + 2\sqrt x \cr
& y = \sqrt 2 \cdot \sqrt x + 2 \cdot \sqrt x \cr
& y = \left( {2 + \sqrt 2 } \right)\sqrt x \cr
& y' = \frac{{2 + \sqrt 2 }}
{{2\sqrt x }} \cr
& y' = \frac{{\sqrt 2 + 1}}
{{\sqrt 2 \sqrt x }} \cr
& y' = \frac{{\sqrt 2 + 1}}
{{\sqrt {2x} }} \cr}
$