Finding Derivative Using 'Definition of Derivative'

1. The problem statement, all variables and given/known data



2. Relevant equations
As seen above in question.


3. The attempt at a solution
Well, I substituted f(x) into the definition of derivative equation and then multiplied the expression by its conjugate, thus getting the expression in the following form:
f'(a) = lim (a + h)^2/3 - a^2/3 / h [(a + h)^1/3 + a^1/3]
..........h→0

Now, from this point on, it's just algebra and I am having trouble manipulating this expression so that I can divide the "h" from the denominator. I know I am supposed to use the "hint" given in the question but how would I incorporate that into finding the answer?


Thanks.

 

I did that but it ended up getting to this expression after some simplifications:
[ (x + h)^2/3(x)^1/3 - (x + h)^2/3(x)^1/3 ] / h
as h → 0.

You can already see what the problem is here. The numerator results in 0, which is subsequently divided by h.