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 ...

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  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 <math>f:f(x) = x^2</math> is <math>f':f'(x) = 2x</math>
  6. The value of this function for a given value of its independent variable.
    The derivative of <math>f(x) = x^2</math> at x = 3 is <math>f'(3) = 2 * 3 = 6</math>.


  1. Obtained by derivation; not radical, original, or fundamental.
    a derivative conveyance; a derivative word
  2. Imitative of the work of someone else.
  3. Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.
  4. Having a value that depends on an underlying asset of variable value.
  5. Lacking originality.

The above text is a snippet from Wiktionary: derivative
and as such is available under the Creative Commons Attribution/Share-Alike License.

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