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Finding a derivative from the limit definition

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of f(x)=x1/3 using the limit definition of a derivative.

    2. Relevant equations

    3. The attempt at a solution

    I am stuck once I plug the numbers into the limit definition equation. How can I simplify the numerator in such a way the the h in the denominator will cancel when both the numbers in the number are cube roots?
  2. jcsd
  3. Sep 11, 2010 #2


    Staff: Mentor

    Show us what you have and where you're stuck.

    You're going to want to use this idea : (a - b)(a2 + ab + b2) = a3 - b3. This formula can be modified to work with cube roots, like so. (a1/3 - b1/3)(a2/3 + a1/3b1/3 + b2/3) = a - b.
  4. Sep 11, 2010 #3
    Edit: Don't worry, Mark got it better than me
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