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
By using the chain rule
, the update law of [W.sub.rj] is
In , 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.
Osler, Leibniz rule, the chain rule
and taylors theorem for fractional derivatives [Ph.D.
Using Lemmas 7 and 8 and the chain rule
we find that the derivative of A is
Concept of a function, derivative, integral, chain rule
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).
In the function notation, the chain rule
indicates: h'(x) = f(g(x)) x g(x).
The readers are invited to find analogous pictures for the chain rule
, related rates, and integration by parts.
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.
Practice the golden supply chain rule
: "Treat your suppliers the way you want your customers to treat you."
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.