Does f(x) is differentiable

Question

I need to determine whether the following function is differentiable at $x_0 \ne 0$ according to the derivative definition:

$$ f(x) = x^\frac{1}{3} $$

So I started by looking at the definition but not sure how to proceed: $$ f'(x_0) =\lim_{x \to x_0} \frac{x^\frac{1}{3} - x_0^\frac{1}{3}}{x - x_0} $$

Thank you

Answer 1

Do u know the formula of a^3 - b^3 ? Then use it .rest is easy.