# Exact sequence of sheafs

I am not quite sure whether my solution for this exercise is correct, more precisely the part $$d: \mathcal{O} \rightarrow \Omega$$.

My solution: each holomorphic 1-form $$\omega$$ is locally exact (because it is closed) and therefore there exists $$f \in \mathcal{E}(X)$$, s.t. $$\omega=df$$. Trivially $$f$$ has to be holomorphic.

Is that correct?