Derivatives. Fun, honestly. Anyways ...
Here's I would do it.
Take the radical out
1/(x+2)^(1/2)
Put it on top
(x+2)^(1/2)
Apply power rule
(1/2)(x+2)^((1/2)-1)
((x+2)^(-1/2))/2
Put it on the bottom
1/(2(x+2)^(1/2))
Put it back in radical form
1/(2√(x+2))
Hope I explained it well for you!