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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
Discrete differential calculus is the study of the definition, properties, and applications of the difference quotient of a function. The process of finding the difference quotient is called differentiation. Given a function defined at several points of the real line, the difference quotient at that point is a way of encoding the small-scale (i ...
The series can be compared to an integral to establish convergence or divergence. Let : [,) + be a non-negative and monotonically decreasing function such that () =.If = <, then the series converges.
This is useful, for example, if the vector-valued function is the position vector of a particle through time, then the derivative is the velocity vector of the particle through time. In complex analysis , the central objects of study are holomorphic functions , which are complex-valued functions on the complex numbers where the Fréchet ...
However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields.
In calculus, the derivative of any linear combination of functions equals the same linear combination of the derivatives of the functions; [1] this property is known as linearity of differentiation, the rule of linearity, [2] or the superposition rule for differentiation. [3]
The q-derivative of a function f(x) is defined as [1] [2] [3] () = ().It is also often written as ().The q-derivative is also known as the Jackson derivative.. Formally, in terms of Lagrange's shift operator in logarithmic variables, it amounts to the operator
Leibniz's concept of infinitesimals, long considered to be too imprecise to be used as a foundation of calculus, was eventually replaced by rigorous concepts developed by Weierstrass and others in the 19th century. Consequently, Leibniz's quotient notation was re-interpreted to stand for the limit of the modern definition.