Formula for curvature of tensor product of connections

Statement

Suppose $E,E'$ are vector bundles over a differential manifold $M$ . Suppose $\nabla ,\nabla '$ are connections on $E,E'$ respectively. Let $R_{\nabla }$ denote the Riemann curvature tensor of $\nabla$ and $R_{\nabla }'$ denote that Riemann curvature tensor of $\nabla '$ . Then if $E\otimes E'$ is the tensor product of vector bundles, $\nabla \otimes \nabla '$ is the tensor product of connections, and $R_{\nabla \otimes \nabla '}$ is its Riemann curvature tensor, we have:

$R_{\nabla \otimes \nabla '}(X,Y)(s\otimes s')=R_{\nabla }(X,Y)(s)\otimes s'+s\otimes R_{\nabla }(X,Y)s'$ .