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  2. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    Properties of the derivative have inspired the introduction and study of many similar objects in algebra and topology; an example is differential algebra. Here, it consists of the derivation of some topics in abstract algebra, such as rings, ideals, field, and so on. [53] The discrete equivalent of differentiation is finite differences.

  3. Derivation (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Derivation_(differential...

    It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. The Pincherle derivative is an example of a derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K ...

  4. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.

  5. Third derivative - Wikipedia

    en.wikipedia.org/wiki/Third_derivative

    In calculus, a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing. The third derivative of a function y = f ( x ) {\displaystyle y=f(x)} can be denoted by

  6. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    In abstract algebra, the product rule is the defining property of a derivation. In this terminology, the product rule states that the derivative operator is a derivation on functions. In this terminology, the product rule states that the derivative operator is a derivation on functions.

  7. Differential (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Differential_(mathematics)

    The simplest example is the ring of dual numbers R[ε], where ε 2 = 0. This can be motivated by the algebro-geometric point of view on the derivative of a function f from R to R at a point p. For this, note first that f − f(p) belongs to the ideal I p of functions on R which vanish at p.

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