Given the limit definition :

$\displaystyle m= \lim_{\Delta x\rightarrow 0} f(x) = (x+\Delta x)- f(x) / \Delta x$

( / means all divided by $\displaystyle \Delta x$) how can I find the derivative of:

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

Step by step would be helpful.