Differentiate from first principles

  • Thread starter auru
  • Start date
  • #1
auru
10
0

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.
 

Answers and Replies

  • #2
R136a1
343
53
Use the equality

[tex](x-a)(x+a)=x^2 - a^2[/tex]

to simplify the limit.
 
  • #3
dirk_mec1
761
13
Simplify the fraction, let h go to zero and you're done.
 
  • #4
auru
10
0
I've done it now, thanks!
 

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