# Finding derivative from limit definition

• May 29th 2009, 08:05 PM
AMaccy
Finding derivative from limit definition
Given the limit definition :

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

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

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

Step by step would be helpful. :)
• May 29th 2009, 08:28 PM
Calculus26
See attachment
• May 29th 2009, 08:40 PM
Random Variable
$\lim_{\Delta x\rightarrow 0} \frac {\sqrt{(x+\Delta x)+2} - \sqrt {x+2}}{\Delta x}$

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

and go from there