## DERIVATIVE

### Derivative

In mathematics, and more specifically in its sub-area named calculus, the derivative is a fundamental tool for the study of the functions of a real variable, which appear everywhere in mathematics, physics and many other sciences. Loosely speaking, the derivative of a function is the ratio of the variation of the value of the function by the variation of its input, when this latter variation is very small, more exactly infinitesimal. For example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity, and the derivative of its velocity is its acceleration. The slope of a road is the derivative ...

The above text is a snippet from Wikipedia: Derivative

### derivative

#### Noun

1. Something derived.
2. A word that derives from another one.
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. The derived function of a function.
The derivative of [itex]f:f(x) = x^2[/itex] is [itex]f':f'(x) = 2x[/itex]
6. The value of this function for a given value of its independent variable.
The derivative of [itex]f(x) = x^2[/itex] at x = 3 is [itex]f'(3) = 2 * 3 = 6[/itex].