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In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. [1] It is one of the two traditional divisions of calculus, the other being integral calculus —the study of the area beneath a curve.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.More precisely, if = is the function such that () = (()) for every x, then the chain rule is, in Lagrange's notation, ′ = ′ (()) ′ (). or, equivalently, ′ = ′ = (′) ′.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and () The quotient rule states that the derivative of h(x) is
In calculus, the differential represents the principal part of the change in a function = with respect to changes in the independent variable. The differential is defined by = ′ (), where ′ is the derivative of f with respect to , and is an additional real variable (so that is a function of and ).
The study of differential calculus is unified with the calculus of finite differences in time scale calculus. [ 53 ] The arithmetic derivative involves the function that is defined for the integers by the prime factorization .
Differential of a function – Notion in calculus; ... Derivative calculator with formula simplification This page was last edited on 28 January 2025, at ...
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