Do functions distribute over the wedge product?

I am wrapping my head around the arithmetic properties of the wedge product. I understand that constants do distribute over the wedge product, i.e. for $c_1,c_2\in\mathbb{R}$, it holds\begin{equation}c_1 \omega_1 ∧ c_2 \omega_2 = (c_1\cdot c_2) \omega_1 ∧ \omega_2 \end{equation}Does this still apply, when the coefficients are functions? Does the following equation hold?\begin{equation}(\cos(x) dx) ∧ (y dz) = (\cos(x)\cdot y) dx∧dz\end{equation}Thank you very much in advance!