Let $\omega = xy \, dx + z \, dy - yz \, dz$ be the $1$-form. Calculate $d\omega$. So I have
\begin{align} d \omega &= (y \, dx + x \, dy) \, \wedge dx + dz \, \wedge dy - (z \, dy + y \, dz) \, \wedge dz \\ &=y \, dx \, \wedge dx + x \, dy \, \wedge dx + dz \, \wedge dy - z \, dy \wedge dz - y \, dz \wedge dz \\ &=x \, dy \wedge dx + (1+z) \, dz \wedge dy && \text{as $da \, \wedge da =0$, $da \, \wedge db = - db \, \wedge da$} \end{align}
Did I compute it correctly? I know I ended up with a $2-$form so something I did was correct.