derivative

Definitions

1. Something derived.
2. A word formed by derivation, such as stylish from style.
3. A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
4. A chemical derived from another.
5. 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.
6. 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 (df)/(dx) in Leibniz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time).
7. The value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain.
8. Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.
9. The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator.

Equivalents

Examples

“The derivative of x² is 2x; if f(x)#61;x², then f'(x)#61;2x”

“The derivative of f(x)#61;x³ at x#61;2 is 12.”

CEFR level