Assume that we have $N$ differentiable functions $f_1(x)$, $f_2(x)$, $\cdots$, and $f_N(x)$. Prove that if $f(x)=f_1(x)+f_2(x)+\cdots+f_N(x)$ then $f'(x)=f'_1(x)+f'_2(x)+\cdots+f'_N(x)$.