How do I find the derivative of f(x) = sqrt(x) without using the power rule?

[Codester09]

Homework Statement

Find the derivative of the function f(x) = sqrt(x).

(Bear in mind that cannot use the power rule or anything like it. I must use lim_h->0.)

Homework Equations

lim_h->0 (f(x+h) - f(x))/h

The Attempt at a Solution

I'm getting hung up on expanding out the sqrt(x+h) term. I'm having trouble with exponents less than 1.

 

[Dick]

Write out the difference quotient and multiply numerator and denominator by sqrt(x-h)+sqrt(x). That's the usual trick.

 

[Codester09]

Yea, you're definitely right. Thanks! Been a while since I had to do that.