I am having a question on the wikipedia article https://en.wikipedia.org/wiki/Second_covariant_derivative
Using the notation therein I don't get why $(\nabla_{u}\nabla_{v}w )^a=u^c\nabla_{c}v^b\nabla_{b}w^a$.
It is clear that $(\nabla_{u}\nabla_{v}w )^a=(u^c\nabla_{c}v^b\nabla_{b}w)^a$.
What do I miss?