Apollonius of Perga
The concept of a derivative in the sense of a tangent line is a very old one, familiar to Greek geometers such as Euclid (c. 300 BC), Archimedes (c. 287–212 BC) and Apollonius of Perga (c. 262–190 BC). Archimedes also made use of indivisibles, although these were primarily used to study areas and volumes rather than derivatives and tangents (see "The Method of Mechanical Theorems").