One of the most important, core concepts in modern mathematics and calculus is the derivative of a function—or a function derived from another function. A derivative is also expressed as the limit of Δy / Δx, also said as “the derivative of y with respect to x.” It is actually the rate of change (or slope on a graph) of the original function; the derivative represents an infinitesimal change in the function with respect to the parameters contained within the function.

In particular, the process of finding the derivative of the function y = f(x) is called differentiation. The derivative is most frequently written as dy / dx; it is also expressed in various other ways, including f'(x) (said as the derivative of a function f with respect to x), y’, Df(x), df(x), or D_xy. It is important to note that the differentials, written as dy and dx, represent singular symbols and not the products of the two symbols. Not all derivatives exist for all values of a function; the sharp corner of a graph, in which there is no definite slope—and thus no derivative—is an example.