I am familiar with the property that expands the exterior derivative acting on the wedge product of two forms,
$$d(\alpha \wedge \beta) = d \alpha \wedge \beta + (-1)^p \alpha \wedge d \beta$$
where $\alpha$ is a p-form and $\beta$ is a q-form.
Can this be generalized in the case
$$d(\alpha \wedge \beta \wedge \gamma)$$
with $\gamma$ being a z-form, and if yes what is the relevant formula?
And can this also be generalized for more terms in the wedge product? Something like $d(\alpha \wedge \beta \wedge \gamma \wedge \cdots)$?
I have tried to find the answer online but I have not been successful.