Differentiate from first principles

  • Thread starter auru
  • Start date
  • #1
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
342
51
Use the equality

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

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

Related Threads on Differentiate from first principles

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
8
Views
2K
Replies
4
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
11K
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
2
Views
965
Replies
2
Views
4K
Replies
15
Views
2K
Top