The Derivative of the Sum of a Finite Number of Differentiable Functions.

Problem: 

Assume that we have N differentiable functions f1(x), f2(x), , and fN(x). Prove that if f(x)=f1(x)+f2(x)++fN(x) then f(x)=f1(x)+f2(x)++fN(x).

Answer: