Let $X$ be a smooth projective variety over a field $k$ of characteristic zero. Consider the hypercohomology in degree one of the logarithmic de Rham complex

$\mathbb{H}^1(X, \mathcal{O}_X^\ast \to \Omega^1_X \to \Omega^2_X \to \cdots)$

where the first arrow $d\log: \mathcal{O}_X^\ast \to \Omega^1_X$ sends $f$ to $\frac{f'}{f}$ (which is closed).

**Question**: Why is this isomorphic to $H^0(X, \Omega^1_X /d\log \mathcal{O}_X^\ast)$?