Using Definition Of Derivative As A Limit to Calculate...

Figured it out, but if you're interested, question is below. It's much easier to do if you solve for f'x not f'2

f'(2) for the function f(x) = 1/(sqrt(x+2))

This problem is teasing me. No matter what approach I take, I cannot make all the numerator terms have enough delta x values to cancel with the quotient delta x terms. I have tried deriving f'(2) with no luck. I know what the limit definition of the derivative is, I'm assuming that is my algebra and ability to manipulate equations that is lacking. Any help is appreciated.