Suppose that $f_k$ is a sequence of differentiable functions that converges uniformly to a function $f$. Must $f$ be differentiable?

Question

Suppose that $f_k: (0,1) \rightarrow \mathbb{R}$ is a sequence of differentiable functions that converges uniformly to a function $f: (0,1) \rightarrow \mathbb{R}$. Must $f$ be differentiable?

So I'm pretty sure this isn't true but struggling to find a simple counterexample.