$y'=(\frac{\sqrt{x+2}+\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-2}})'$
$y'=\frac {\frac {1}{2\sqrt{x+2}}+\frac {1}{2\sqrt {x-2}}}{\frac {1}{2\sqrt{x+2}}-\frac {1}{2\sqrt {x-2}}} $
$y'=\frac {\sqrt {x-2}-\sqrt {x+2}}{\sqrt {x-2}+\sqrt {x+2}}$
$y'=\frac {-4}{(\sqrt {x-2}+\sqrt {x+2})^2}$