I'm feeling an induction proof coming on. It's not like they are infinite sums. You won't have to worry about convergence.
Maybe I'm wrong.
No, completely right. Induction on n and the "sum rule": (f(x)+ g(x))'= f'(x)+ g'(x).
I'm not sure how to proceed with induction.
Because , what needs to be proven is that . The same goes to .