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Derivative from Definition (square roots)

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the derivative from definition of the functin f(x)= x + squareroot(x)

    2. Relevant equations

    3. The attempt at a solution
    I only got as far as where I cancelled out my positive and negative x terms in the numerator, and am left with three terms (2 of which are square roots, the other being an h), and I am wondering what to do now; is there some way to multiply by the conjugate?
  2. jcsd
  3. Sep 27, 2008 #2


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    Homework Helper

    The difference quotient should look like

    \frac{((x+h) + \sqrt{x+h}) - (x + \sqrt x)}{(x+h)-x} = \frac{h + (\sqrt{x+h} - \sqrt x)}{h},

    does it not? try splitting it into 2 fractions (based on the grouping I've shown above). One of the fractions is quite simple, the other you can simplify with the method you mentioned in your post. After the fractions are simplified, bring in the limits as [tex] h \to 0 [/tex]
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