Consider the forms

$\displaystyle \omega =xy dx +3dy - yz dz$

$\displaystyle \eta = xdx - yz^2 dy +2x dz$,

in $\displaystyle \mathbb{R}^3$. Verify by direct computations that

$\displaystyle d(d\omega) = 0$ and $\displaystyle d(\omega \wedge \eta) = (d\omega) \wedge \eta -\omega \wedge d\eta$

Probably doing a mistake in computations

Please, help