What is the Derivative of y = √x at x = 1?

[fiziksfun]

I was asked to find the derivative of y=sqrtx at x=1

I need to use the formula

lim x -> a = f(x) - f(a) / (x-a) to find the derivative at x=1

I have..

sqrtx - 1 / (x - 1) BUT i can't simply it from there. Help!

THANKSZ.

 

[arildno]

Okay:
$$\frac{\sqrt{x}-1}{x-1}=\frac{\sqrt{x}+1}{\sqrt{x}+1}\frac{\sqrt{x}-1}{x-1}=\frac{(\sqrt{x}+1)(\sqrt{x}-1)}{x-1}\frac{1}{\sqrt{x}+1}$$
Does that help you a bit?