= Gauge transformation in the derivative-plus-connection convention
{title2=$\delta A_\mu=-\partial_\mu\Lambda+[\Lambda,A_\mu]$}
For $D_\mu=\partial_\mu+A_\mu$ and $\delta\phi=\Lambda\phi$, covariance requires $\delta A_\mu=-\partial_\mu\Lambda+[\Lambda,A_\mu]$. Expanding $[D_\mu,D_\nu]$ gives $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu+[A_\mu,A_\nu]$, and operator Jacobi gives $\delta F_{\mu\nu}=[\Lambda,F_{\mu\nu}]$. An invariant internal quadratic form makes its Yang-Mills kinetic contraction gauge invariant. Couplings and factors of i are absorbed into the connection in this convention.
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