The derivative in four stages: Fermat to Cauchy | Tangente

• The derivative was first used in the 17^th century, notably by Fermat when he devised a method for finding the maximum or minimum of a function. The mathematician from Toulouse showed that, in most cases, the presence of an extremum implies that what would later be called the derivative of the function is zero.

• It was then discovered with the birth of mathematical analysis, generally credited to Newton and Leibniz. It was Leibniz who gave the term "derivative" its mathematical meaning.

• Their successors then explored and developed it, notably Joseph-Louis Lagrange, who studied series expansions whose terms involve successive derivatives.

• Finally—and only then—it was defined using the concept of a limit. Illustrious 19^th century mathematicians such as Augustin Louis Cauchy and Karl Theodor Wilhelm Weierstrass laid the foundations for the definition we use today.