Question on definition of a connection

Question

in my exercise we have a connection defined on the trivial bundle $E=M \times \mathbb{R}^N$, $\nabla=d+A$ where $A \in\Omega^1(M, gl_N(\mathbb{R})$. Now we don't have any explanation what $d$ is supposed to be, I assume its somehow the differential operator but I don't know how to interpret it... can somebody help me with this?

Answer 1

If $\sigma$ is a section of $E$, and $X$ a vector field on $N$, $\nabla_X\sigma=d\sigma(X)+A(X)$.