The question means: find a closed form expressions for , by closed form we mean a finite representation with no infinite series etc in it.
As has been pointed out elsewhere in this thread we have:
Integrating this gives:
Now we know that , so we have:
f'(x) = a geometric series.
There is a formula for this: 1/(1-r), where r is the common ratio. So now you can rewrite f'(x).
"How is f' related to f ?" - you integrate f' to get f.
Where was the trouble in this process for you?