# Definition of "derivative"

## derivative

### adjective

*comparative*more derivative,*superlative*most derivative### noun

*plural*derivatives(calculus) One of the two fundamental objects of study in calculus (the other being integration), which quantifies the rate of change, tangency, and other qualities arising from the local behavior of a function.

(Of a function of a single variable f ( x )) The derived function of f ( x ) : the function giving the instantaneous rate of change of f ; equivalently, the function giving the slope of the line tangent to the graph of f . Written f ′ ( x ) or d f d x in Leibniz's notation, f ˙ ( x ) in Newton's notation (the latter used particularly when the independent variable is time).

(Of more general classes of functions) Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.