For a $k$ form $\eta$ and a $l$ form $\omega$, what is $d(\eta\wedge\omega)?$

Question

For a $k$ form $\eta$ and a $l$ form $\omega$, what is $d(\eta\wedge\omega)?$ Thank you very much for your help and guidance!

Answer 1

Use the Leibniz rule, i.e.

$$d(\eta\wedge\omega)=d\eta\wedge\omega+(-1)^{k}\eta\wedge d\omega.$$

It is one of the properties satisfied by the operator $d$.