TeXipedia

prime

Denotes a derivative or modified version of a variable, commonly used in mathematics and physics notation.

Overview

Essential for mathematical notation across various disciplines, particularly when indicating derivatives, complementary elements, or alternative versions of variables.

  • Widely used in calculus to denote derivatives (e.g., f′(x))
  • Common in physics for denoting transformed coordinates or modified quantities
  • Appears in algebra to distinguish related variables (e.g., x and x′)
  • Used in set theory to indicate complementary or related sets
  • Frequently combined with letters in both subscript and superscript positions

Examples

Denoting a first derivative of a function.

f′(x)=2xf^{\prime}(x) = 2x 
f^{\prime}(x) = 2x

Using multiple primes to show higher derivatives.

f′′′(x)=sin⁡(x)f^{\prime\prime\prime}(x) = \sin(x) 
f^{\prime\prime\prime}(x) = \sin(x)

Indicating a transformed or related variable.

x′=x+hx^{\prime} = x + h 
x^{\prime} = x + h