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We extend a classical fact about deformations of groups of units ofcommutative rings to $\mathbb{E}_{\infty}$-ring spectra, and we use this resultto provide a map of spectra generalizing the ordinary logarithmic derivativeinduced by an $R$-module derivation.

Deformations of $\mathbb{E}_{\infty}$-groups of units and logarithmic derivatives of $\mathbb{E}_{\infty}$-rings