Changes

A '''derivative''' is a measure in [[Calculus]] of how functions change based on how their input values change; otherwise known as 'the rate of change' (second derivatives thus give the rate of change of change, etc). For example, [[speed]] is a first derivative, obtained from distance and time, whereas [[acceleration]] is a second derivative, obtained from the first derivative, speed, and time.

A '''derivative''' is a measure in [[Calculus]] of how functions change based on how their input values change; otherwise known as 'the rate of change' (second derivatives thus give the rate of change of change, etc). For example, [[velocity]] is obtained from taking the first [[derivative]] of a [[position]] [[function]] with respect to time.  [[Acceleration]] can be obtained either by taking the [[derivative]] of a [[velocity]] [[function]] with respect to time or by taking the time [[derivative]] of a [[position]] [[function]] twice.  Note that when using this method, taking the derivative the first time yields the [[velocity]] function, and taking the derivative the second time yields the [[acceleration]] function.

 

The terms [[speed]] and [[velocity]] are often used interchangeably, which is incorrect.  [[Speed]] is a [[Scalar quantity]] which refers to the magnitude, or size, of the [[velocity]] [[vector quantity|vector]].  [[Velocity]] has a direction, while [[speed]] does not.

  Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point.  

  Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point.