I'm reading Donaldson's book, Floer homology groups in Yang-Mills theory. On page 82, he considers a trivial bundle $P$ over a $4$-manifold $X$ with tubular ends which is equipped with a connection $A_0$ and this connection is flat on each ends. (This is called an adapted bundle in the book.) He writes the covariant derivative induced by $A_0$ as $\nabla_0$ and on page 84, he apply this $\nabla_0$ to a gauge transformation $g$. My question is that since he defines the gauge transformation group as Aut($P$), how we can apply $\nabla_0$ to such an element? I only know how to apply $\nabla_0$ to sections of those vector bundles associated to $P$. And I don't know how I can regard elements in Aut($P$) as such sections? In short, what is $\nabla_0 g$ for $g \in$ Aut($P$)?