Derivative

Calculus · 1675

Equation: f′(x) = df/dx = lim_{h→0} [f(x+h) − f(x)] / h
Field: Calculus
Symbols: f a function · f′ or df/dx its rate of change · h a step that shrinks to nothing
Year: 1675

Significance

The slope of a curve at a single point, obtained by taking the slope over an ever-smaller step. Velocity is the derivative of position, acceleration of velocity, current of charge, power of work; almost every law of physics on this site is a statement about a derivative. Newton had it in 1665 as fluxions; the notation that survived is Leibniz's, from 1675.

Required By

Curvature Fundamental Theorem of Calculus Chain Rule Taylor Series Gradient Kinematic Equations Power Centripetal Acceleration Simple Harmonic Motion Newton's Second Law Newton's Law of Cooling Radioactive Decay Law Elastic Wave Equation Wave Equation Euler–Lagrange Equation Schrödinger Equation Newtonian Viscosity

Referenced by

equation

Centripetal Acceleration Chain Rule Curvature Elastic Wave Equation Euler–Lagrange Equation Fundamental Theorem of Calculus Gradient Kinematic Equations Newton's Law of Cooling Newton's Second Law Newtonian Viscosity Power Radioactive Decay Law Schrödinger Equation Simple Harmonic Motion Taylor Series Wave Equation

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.