Infinitesimal

An infinitesimal or infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. In common speech, an infinitesimal object is smaller than any feasible measurement, but not zero in size, or so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective in mathematics, infinitesimal means infinitely small, smaller than any standard real number. 
The term differential is used (in calculus) to refer to an infinitesimal ('infinitely small') change. E.g. for a variable x, a change in the value of x is often denoted as \Delta x. The differential is an infinitely small change in x, denoted as dx. It is possible to relate infinitesimal changes of variables to each other using derivatives. If 
Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically using derivatives. If y(x)s a function of x, then the differential dy of y is related to the infinitesimal change in x, dx, by the formula dy(x) = \frac{dy(x)}{dx}dx, where the fraction gives the derivative. This formula summarizes the intuitive idea that the derivative is the limit of the ratio of differences\Delta y / \Delta x as \Delta xbecomes infinitely small.
An integral can be regarded as an infinite sum of infinitesimal quantities, the area under a graph is obtained by subdividing the graph into infinitely thin strips and summing their areas. In an expression such as \int f(x) dx, the integral sign denotes the infinite sum, f(x) denotes the "height" of a thin strip, and the differential dxdenotes its infinitely thin width.