Derivative - History And Usefulness

Calculus was first invented by Sir Isaac Newton around 1665. Newton was a physicist as well as a mathematician. He found that the mathematics of his time was not sufficient to solve the problems he was interested in, so he invented new mathematics. About the same time another mathematician, Goltfried Leibnez, developed the same ideas as Newton. Newton was interested in calculating the velocity of an object at any instant. For example, if you sit under an apple tree, as legend has it Newton did, and an apple falls and hits you on the head, you might ask how fast the apple was traveling just before impact. More importantly, many of today's scientists are interested in calculating the rate at which a satellite's position changes with respect to time (its rate of speed). Most investors are interested in how a stock's value changes with time (its rate of growth). In fact, many of today's important problems in the fields of physics, chemistry, engineering, economics, and biology involve finding the rate at which one quantity changes with respect to another, that is, they involve finding the derivative.