Thread: Finding derivative from limit definition

1. Finding derivative from limit definition

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.

2. See attachment

3. $\displaystyle \lim_{\Delta x\rightarrow 0} \frac {\sqrt{(x+\Delta x)+2} - \sqrt {x+2}}{\Delta x}$

$\displaystyle = \lim_{\Delta x\rightarrow 0} \frac {\sqrt{(x+\Delta x)+2} - \sqrt {x+2}}{\Delta x} \frac {\sqrt {(x+\Delta x)+2} + \sqrt {x+2}}{\sqrt{(x+\Delta x)+2}+ \sqrt {x+2}}$

and go from there