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

• Jan 24th 2011, 12:47 PM
evankiefl
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.
• Jan 24th 2011, 12:54 PM
e^(i*pi)
$\displaystyle \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}$

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

Hence $f(x+h) = \dfrac{1}{\sqrt{x+h+2}}$

$\displaystyle \lim_{h \to 0} \dfrac{\dfrac{1}{\sqrt{x+h+2}} - \dfrac{1}{\sqrt{x+2}}}{h}$