Hi, can anyone please help me with this question?

Consider the powerseries:

$\displaystyle f(z)=\displaystyle \sum_{n=0}^{\infty} a_n z^n$

with the property that

$\displaystyle f(\frac{1}{a})=\frac{1}{a^3} \forall n\in\mathbb N$

Prove that

$\displaystyle f'(0)=0$

I had hint to use Uniqueness Theorem of Power Series, but I still have no idea how to do it. Please help me, thanks a lot.