This is an Exercise 6.2.55 in Garth Dales , Introduction to Banach algebra

Show that there are many discontinuous Point derivations on the Banach algebra $ (\mathbb{C^{(n)}[0,1], \|\|_n})$ where $ $ \|f\|_n=\sum_{k=0}^{n}\frac{1}{k!}|f^{(k)}|$ $ for all $ f\in \mathbb{C^{(n)}[0,1]} $

so if you give reasonable hints, I will be very happy. Thanks