let $g\stackrel{\alpha}{\curvearrowright}(m,\tau)$ be a trace-preserving action of a finite group $g$ on a tracial von neumann algebra. suppose that $a \subset m$ is a finitely generated unital $*$-subalgebra which is globally invariant under $\alpha$. we give a formula relating the von neumann dimension of the space of derivations on $a$ valued on its coarse bimodule to the von neumann dimension of the space of derivations on $a \rtimes^{\text{alg}}_\alpha g$ valued on its coarse bimodule, which is reminiscent of schreier's formula for finite index subgroups of free groups. this formula induces a formula for $\dim \text{der}_c(a,\tau)$ (defined by shlyakhtenko) and under the assumption that $g$ is abelian we obtain the formula for $\delta$ (defined by connes and shlyakhtenko). these quantities and the free entropy dimension quantities agree on a large class of examples, and so by combining these results with known inequalities, one can expand the family of examples for which the quantities agree.