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Differentiate from first principles

  1. Oct 31, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    f'(x) = Lim h→0 [f(x+h) - f(x)]/h

    3. 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.
  2. jcsd
  3. Oct 31, 2013 #2
    Use the equality

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

    to simplify the limit.
  4. Oct 31, 2013 #3
    Simplify the fraction, let h go to zero and you're done.
  5. Oct 31, 2013 #4
    I've done it now, thanks!
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