Explore Derivative on MathWorld

A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.

Derivative is a college-level concept that would be first encountered in a Calculus I course. It is an Advanced Placement Calculus AB topic and is listed in the California State Standards for Calculus.


Calculus: Calculus is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects.
Function: A function is a relation that uniquely associates members of one set with members of another set. The term "function" is sometimes implicitly understood to mean continuous function, linear function, or function into the complex numbers.
Limit: A limit is the value a function approaches as the variable approaches some point. If the function is not continuous, the limit could be different from the value of the function at that point.

Classroom Articles on Calculus I (Up to College Level)

  • Chain Rule
  • Inflection Point
  • Continuous Function
  • Integral
  • Critical Point
  • Intermediate Value Theorem
  • Definite Integral
  • Maximum
  • Discontinuity
  • Mean-Value Theorem
  • Extreme Value Theorem
  • Minimum
  • First Derivative Test
  • Newton's Method
  • Fundamental Theorems of Calculus
  • Riemann Sum
  • Implicit Differentiation
  • Second Derivative Test
  • Indefinite Integral