$d/dx$ is not continuous in $L^2$

Question

To show that $\frac{d}{dx}:A \to L^2 (a,b) $ is not continuous, where $$A=\left\{u \in L^2 (a,b): \frac{du}{dx} \in L^2 (a,b) \right\} $$

I'm trying take a map's sussection that $|du_n|>c_n|u_n|$ but I cant find.