Derivatives

Abstract

The concept of the derivative was hidden in the problem of finding the line tangent to a given curve at a given point, a problem tackled by the Greek mathematicians more than two thousand years ago. This concept took definite shape during the years 1665–1666, when the famous English scientist Isaac Newton, the founder of modern physics, developed the process now known as differentiation. At that time, Newton did not publish his work, and the same concept was rediscovered independently by Gottfried Wilhelm Leibniz (1646–1716), a German scholar having expertise in philosophy, law, mathematics, and science. The discovery of the derivative as a fundamental ingredient of calculus completely changed the nature of scientific studies, particularly mathematics. Coupled with Newton’s formulation of the laws of motion and gravitation, the calculus of Newton and Leibniz and their subsequent refinements and extensions revolutionized the modern world.