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The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...
The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for any functions f and g, ′ = () ′ = (′ + ′ ), wherever both sides are well defined. Special cases
Home rule in the United States relates to the authority of a constituent part of a U.S. state to exercise powers of governance; i.e.: whether such powers must be specifically delegated to it by the state (typically by legislative action) or are generally implicitly allowed unless specifically denied by state-level action.
The power is divided into two broad categories: general powers of appointment and special powers of appointment. The holder of a power of appointment differs from the trustee of a trust in that the former has no obligation to manage the property for the generation of income, but need only distribute it.
A derivation is a linear map on a ring or algebra which satisfies the Leibniz law (the product rule). Higher derivatives and algebraic differential operators can also be defined. They are studied in a purely algebraic setting in differential Galois theory and the theory of D-modules , but also turn up in many other areas, where they often agree ...
The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.
Section 551 of the Administrative Procedure Act gives the following definitions: . Rulemaking is "an agency process for formulating, amending, or repealing a rule." A rule in turn is "the whole or a part of an agency statement of general or particular applicability and future effect designed to implement, interpret, or prescribe law or policy."
In sociology, authority is the legitimate or socially approved power which one person or a group possesses and practices over another. The element of legitimacy is vital to the notion of authority and is the main means by which authority is distinguished from the more general concept of power. Power can be exerted by the use of force or violence.