Let $\alpha, \beta$ be $k$-forms, then, where $d$ is the exterior derivative, we have $$ d (\alpha \wedge \beta) = d \alpha \wedge \beta + (-1)^k (\alpha \wedge d \beta)$$
However, in many cases, e.g. this answer, or this textbook (pg. 147), I've come across the equation, when $\alpha, \beta$ are $1$-forms,
$$ d (\alpha \wedge \beta) = d \alpha \wedge \beta + \alpha \wedge d \beta $$
The second equation doesn't agree with the first one, since $(-1)^k=-1$ in our case,where $k$=1.
What am I missing?