Differentially

Differentially is an English adverb formed from the adjective differential. It signals that something is described or analyzed in relation to a difference, a differential, or a change that is treated with respect to a variable or set of variables. The term is most common in technical writing, where precise mathematical or statistical meaning is required.

In mathematics, differentially often appears in contexts involving differentials or infinitesimal changes. For example, one might say that a function changes differentially with respect to x, or that a quantity is measured to a differentially small degree. The phrasing emphasizes a relation to differential calculus rather than just a general difference.

In biology and genomics, differentially expressed is standard terminology. A gene is described as differentially expressed between conditions if its expression level differs significantly, as determined by differential expression analysis.

In computer science and data privacy, differentially private is a formal term. A mechanism is differentially private if the inclusion or exclusion of a single individual's data does not meaningfully affect the output, providing a mathematical privacy guarantee.

Etymology and usage notes: differentially is formed by adding -ly to differential, and it has been used in technical literature since the 19th century. In everyday language, differentially is rare outside specialized domains; in general prose, one would typically say “in a different way” or “differently” unless a precise technical sense is intended.