Induction With The Sum Of $n$ Differentiable Functions

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Problem 74: (Induction With The Sum Of $n$ Differentiable Functions)

In calculus we learned that if $f$ and $g$ are differentiable functions at $x=c$, then $(f+g)'(c) = f'(c)+g'(c)$. Use induction to prove that if $f_1,f_2,\ldots, f_n$ are differentiable functions at $x=c$, then $(f_1+f_2+\cdots+f_n)'(c) = f_1'(c)+f_2'(c)+\cdots+f_n'(c) $.

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