Calculating equation of motion in gauge theories: using ordinary derivatives or covariant derivatives?

For general gauge theories, the total Lagrangian density is given as $$L=-frac{1}{4}F^2+L_M(psi, Dpsi)$$ where $L_M(psi, Dpsi)$ is the matter field with the ordinary derivative replaced by the covariant derivative $D$. Here $psi$ is a generic matter field other than the gauge field.

Then, for calculating the equation of motion for the matter field $psi$, I am confused whether I have to calculate with $partial_mu phi$ or $D_mu psi$. That is, which one is correct?:

begin{equation}
frac{partial L}{partialpsi}-partial_mu frac{partial L}{partial(partial_mupsi)}=0,tag{1}
end{equation}

begin{equation}
frac{partial L}{partialpsi}-D_mu frac{partial L}{partial(D_mupsi)}=0.tag{2}
end{equation}

This kind of stuff have always confused me…so I desperately feel a need to clarify.