Exercise 26.
Let \(f_1, f_2,\ldots, f_n\) be differentiable functions. Prove, using induction, that
\begin{equation*}
(f_1 + f_2 + \cdots + f_n)' = f_1' + f_2' + \cdots + f_n'\text{.}
\end{equation*}
You may assume \((f+g)' = f' + g'\) for any differentiable functions \(f\) and \(g\text{.}\)