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## Homework Statement

Show that if ##a\in D##, ##f,g : D\to \mathbb{R}## are both differentiable and ##x=a##, ##f(a)=g(a)##, and ##f(x)\le g(x)## for all ##x\in D##, then ##f'(a)=g'(a)##

## Homework Equations

## The Attempt at a Solution

I have a proof for this problem already, but I have a naive question. If the two functions are differentiable at ##a## and ##f(a)=g(a)##, why can't we just take the derivative of both sides to show that ##f'(a)=g'(a)##