Differentiate from first principles

[auru]

Homework Statement

Differentiate (x+1)^1/2 from first principles with respect to x.

Homework Equations

f'(x) = Lim h→0 [f(x+h) - f(x)]/h

The Attempt at a Solution

f'(x) = Lim h→0 [f(x+h) - f(x)]/h
f'(x) = Lim h→0 [(x+h+1)^1/2 - (x+1)^1/2]/h

I'm unsure how to simplify from there.

 

[R136a1]

Use the equality

$$(x-a)(x+a)=x^2 - a^2$$

to simplify the limit.

 

[dirk_mec1]

Simplify the fraction, let h go to zero and you're done.

 

[auru]

I've done it now, thanks!