In calculus, what is the opposite of a derivative?
Multiplicative calculus β = I, then the *-calculus is the so-called anaquadratic calculus. Multiplicative calculus In mathematics, a multiplicative calculus is a system with two multiplicative operators, called a "multiplicative derivative" and a "multiplicative integral", which are inversely related in a manner analogous to the inverse relationship between the derivative and integral in the classical calculus of Newton and Leibniz. The multiplicative calculi provide alternatives to the classical calculus, which has an additive derivative and an additive integral. Infinitely many non-Newtonian calculi are multiplicative, including the geometric calculus and the bigeometric calculus discussed below.. These calculi all have a derivative and/or integral
Generalizations of the derivative combine two or more of the above different notions of extension or abstraction of the original derivative. For example, in Finsler geometry, one studies spaces which look locally like Banach spaces. Thus one might want a derivative with some of the features of a functional derivative and the covariant derivative. The study of stochastic processes requires a form of calculus known as the Malliavin calculus. One notion of derivative in this setting is the "H"-derivative of a function on an abstract Wiener space. Multiplicative calculus replaces addition with multiplication, and hence rather than dealing with the limit of a ratio