Disprove: If $ f_n , f $ are differentiable and $ f_n \to f $ uniformly, then $ f_n’ \to f’ $ ( pointwise )

Question

Prove\Disprove: If $ f_n , f $ are differentiable and $ f_n \to f $ uniformly, then $ f_n' \to f' $ ( pointwise ).

I was told the theorem is false but I couldn't come up with an example. Can you please help? how would you find an example that satisfies all the assumptions in question like this, is there some sort of rule-of-thumb I don't know about?

Answer 1

Try $f_n(x) = \frac{sin {nx}}{n}$ with $f(x) = 0$