Finding a derivative from the limit definition

[Jimmy25]

Homework Statement

Find the derivative of f(x)=x^1/3 using the limit definition of a derivative.

Homework Equations

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?

 

[Mark44]

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. (a^1/3 - b^1/3)(a^2/3 + a^1/3b^1/3 + b^2/3) = a - b.

 

[RK1992]

Edit: Don't worry, Mark got it better than me