Leibniz notation

Leibniz notation is a system of calculus symbols, including dy/dx and ∫, introduced by Gottfried Wilhelm Leibniz. It expresses derivatives and integrals in forms that reveal relationships among changing quantities and accumulated values.

Derivative: A measure of how a function's output changes as its input changes. The derivative is the operation represented by dy/dx.
Derivative notation: A collection of symbols for derivatives, including prime, operator, and differential forms. Leibniz notation is the differential form used to write derivatives.
Gottfried Wilhelm Leibniz: A German philosopher and mathematician who independently developed calculus and introduced its enduring notation. His symbols dy/dx and ∫ gave the notation its name.
Lagrange notation: A derivative notation using primes, such as f′, to mark successive derivatives of a function. It marks derivative order compactly but does not display input and output differentials.
Related rates: A calculus method for finding how quantities change together over time. Differential notation clearly relates the rates of changing variables.
Differential: A quantity representing an infinitesimal change in a variable or function. The symbols dy and dx denote changes whose relationship dy/dx expresses.
Chain rule: A rule for differentiating a composition of functions. Leibniz notation displays the intermediate differentials that compose under this rule.
Isaac Newton: An English mathematician and physicist who independently developed calculus using quantities called fluxions. Newton's fluxion notation offered a competing language for calculus.
Newton notation: A derivative notation using dots above variables to indicate time derivatives. It is concise for time-dependent quantities but less suited to arbitrary independent variables.
Ordinary differential equation: An equation involving an unknown function of one variable and its derivatives. Expressions such as dy/dx state the rates constrained by these equations.

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