Definition

1. Noun:
   • The result of mathematical differentiation: In calculus, the "derived function" is the function obtained by differentiating another function. It represents the rate at which the original function's value changes.
   • The instantaneous rate of change: It measures how one quantity changes instantaneously relative to a change in another quantity, often expressed as df(x)/dx or f'(x).

Usage Examples

• Noun:
  • To find the slope of the curve at any point, you must calculate the derived function.
  • The derived function of position with respect to time is velocity.

Advanced Usage

• Fundamental Concept in Calculus: The derived function is central to differential calculus, used for finding tangents, optimizing functions, and modeling rates of change in physics, economics, and engineering.
• Notation: Commonly denoted as f'(x), dy/dx, or df/dx. The process of finding it is called "differentiation."

Variants and Related Words

• Derivative (n): The most common synonym for "derived function." ()
• Differentiation (n): The mathematical operation of finding a derived function.
• Differential Calculus (n): The branch of calculus concerned with derivatives and their applications.

Synonyms

• Derivative
• Differential Coefficient
• Rate-of-change function

Related Phrases

• First derived function: The derivative obtained from the first differentiation.
• Higher-order derived function: A function obtained by differentiating a derived function multiple times (e.g., second derivative f''(x)).

Noun

1. the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx