Hi all,

I am in an early calculus chapter, where I am finding derivatives algebraically. (Hence why I am posting in pre-calculus; I have not yet covered techniques to differentiate functions efficiently.) I am asked to find the differential of the following function:

$\displaystyle {f}(x) = \frac{1}{\sqrt{x+2}}$

I am trying to find the derivative by using a limit function to determine instantaneous rate of change:

$\displaystyle {f}'(x) = \lim_{h \to 0} \left ( \frac{1}{h} \right ) \left (\frac{1}{\sqrt{x + h + 2}} - \frac{1}{\sqrt{x + 2}} \right )$

However, I cannot solve this equation--I don't know how to get an 'h' factor in the numerator, which would allow me to cancel out the (1 / h) term. I have tried multiplying, dividing, and subtracting terms; I have tried multiplying the conjugates of radicals; I've been at this one for a while. Hopefully, one of you thinks this is obvious, and I've already over-explained a very simple problem... I've been staring at this one too hard, and I'm definitely missing the trick.

Thank you!