chain rule

[′chān ‚rül]

(mathematics)

A rule for differentiating a composition of functions: (d/dx) ƒ (g (x)) = ƒ′(g (x))· g ′(x).

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Chain Rule

a method given in old arithmetic textbooks for converting the measures of one system into the measures of another system by means of a third system.

Suppose, for example, we want to know the number of vershki equal to 3 feet if 1 foot is equal to 12 inches and 28 inches are equal to 16 vershki. To apply the chain rule, we write the elements of the problem in the following form:

x vershki	3 feet
1 foot	12 inches
28 inches	16 vershki

The required number of vershki is obtained by dividing the product of the numbers in the right-hand column by the product of the known numbers in the left-hand column:

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References in periodicals archive

If f [member of] [C.sup.1](R, R) and g : T [right arrow] R is delta differentiable, then the time scales chain rule, see [5, Theorem 1.90], states that

Improvements of dynamic Opial-type inequalities and applications

By using the chain rule, the update law of [W.sub.rj] is

Intelligent control for USV based on improved Elman neural network with TSK fuzzy

In [7], the authors used the following chain rule [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to convert a fractional differential equation with Jumarie's modification of Riemann-Liouville derivative into its classical differential partner.

A novel analytical technique to obtain kink solutions for higher order nonlinear fractional evolution equations

Osler, Leibniz rule, the chain rule and taylors theorem for fractional derivatives [Ph.D.

New expansion formulas for a family of the [lambda]-generalized Hurwitz-Lerch Zeta functions

Using Lemmas 7 and 8 and the chain rule we find that the derivative of A is

Stationary points--I: one-dimensional p-Fuzzy dynamical systems

Concept of a function, derivative, integral, chain rule, arclength.

Model-based assessment of conceptual representations

When [partial derivative]E([theta]) / [partial derivative][p.sub.k] = [partial derivative]E[theta] / [partial derivative]y [partial derivative]y / [partial derivative][p.sub.k] is determined with chain rule, this gives partial derivative]y / [partial derivative][p.sub.k] = [[theta].sub.k][x.sup.Pk] ln(x).

Polynomial curve fitting with varying real powers/Polinominiu kreiviu pritaikymas keiciantis realiai galiai

In the function notation, the chain rule indicates: h'(x) = f(g(x)) x g(x).

Cognitive development of applying the chain rule through three worlds of mathematics

The readers are invited to find analogous pictures for the chain rule, related rates, and integration by parts.

Literally changing the point of view

This third edition offers three new chapters on fixed- or finite-memory filters, use of the chain rule from calculus for filter initialization, and use of a bank of linear sine-wave Kalman filters for estimating the actual frequency of noisy sinusoidal measurements.

Fundamentals of Kalman filtering; a practical approach, 3d ed

For available local partial derivatives of the arithmetic operators and intrinsic functions provided by the programming language, the Jacobian of the function at the given arguments can be accumulated by using the chain rule. This technique is known as automatic differentiation of numerical programs.

Optimality-preserving elimination of linearities in Jacobian accumulation