In several texts, the luminary Eleleth is the last of the luminaries ( Spiritual Lights ) that come forward, and it is the Aeon Sophia, associated with Eleleth, who encounters darkness and becomes involved in the chain of events that leads to the Demiurge's rule of this world, and the salvage effort that ensues.

The material derivative of, using the chain rule, is then

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.

That is, if f is a function and g is a function, then the chain rule expresses the derivative of the composite function in terms of the derivatives of f and g.

In integration, the counterpart to the chain rule is the substitution rule.

The chain rule seems to have first been used by Leibniz.

The common notation of chain rule is due to Leibniz.

L ' Hôpital uses the chain rule implicitly in his Analyse des infiniment petits but also does not state it explicitly.

The chain rule does not appear in any of Leonhard Euler's analysis books, even though they were written over a hundred years after Leibniz's discovery.

The chain rule gives a method for computing in terms of and.

The utility of the chain rule is that it turns a complicated derivative into several easy derivatives.

The chain rule states that, under appropriate conditions,

In the statement of the chain rule, f and g play slightly different roles because f ′ is evaluated at g ( t ) whereas g ′ is evaluated at t. This is necessary to make the units work out correctly.

The factor g ′( 10 ) in the chain rule is the velocity of the skydiver ten seconds after his jump, and it is expressed in meters per second.

The simplest form of the chain rule is for real-valued functions of one real variable.

It may be possible to apply the chain rule even when there are no formulas for the functions which are being differentiated.

To find the temperature drop per hour, we apply the chain rule.

The chain rule says that the derivative of the composite function is the product of the derivative of f and the derivative of g. This is.

The chain rule can be applied to composites of more than two functions.

The chain rule says that to compute the derivative of, it is sufficient to compute the derivative of f and the derivative of.

The derivative of f can be calculated directly, and the derivative of can be calculated by applying the chain rule again.

The chain rule says that the derivative of their composite at the point is:

Another way of computing this derivative is to view the composite function as the composite of and h. Applying the chain rule to this situation gives:

The chain rule can be used to derive some well-known differentiation rules.

Ah, he thought, she's going through the chain of reasoning which says she might really just as well pick up my shorts too.

If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:

Della then shows Jim the chain she bought for him, to which Jim says he sold his watch to get the money to buy her combs.

Foley's, a chain of department stores in Texas owned by Macy's, in Cincinnati, says operations in McAllen and nearby Laredo are its fastest-growing locations.

J. C. Penney says about three quarters of customers at its McAllen store are from Mexico and last year the chain allowed Mexican shoppers to apply for its gift registry and credit card.

On Friday, January 13, 2012, Dish CEO Joseph Clayton announced that while Dish originally planned to keep 90 percent of the stores in operation ( roughly 15, 000 employees got to keep their jobs ), due to market factors Clayton says he still wants to keep the Blockbuster chain going but, “ there are ones that aren't going to make it.

Antipholus is forced to accept the chain, and Angelo says that he will return for payment.

The Courtesan spies Antipholus wearing the gold chain, and says he promised it to her.

Before that he gave disco lessons at sororities and says he paid for his junior year with a chain letter.

In " The Pothole " ( 1997 ), a Phil Rizzuto key chain is featured that says " Holy Cow!

# Arrangement in this form: Group of side chains and secondary functional groups with numbers made in step 3 + prefix of parent hydrocarbon chain ( eth, meth ) + double / triple bonds with numbers ( or " ane ") + primary functional group suffix with numbers. Wherever it says " with numbers ", it is understood that between the word and the numbers, the prefix ( di -, tri -) is used.

The United State Navy says, " Submarines require no vulnerable underway logistics chain nor depend on mutual defense from other platforms for survivability.

At the studio, an expert, Dr. Nils Johannsen, brought in by RBS ( remotely ) says that there are conventional explosives in the device, geared to set up the chain reaction.

" has been screamed ( thus a repetition ), so the one with the phobia of repetition screams, the one with the problem of barking at other peoples phobia barks next to the ear of the person with the phobia of apologies, scaring him and then he says sorry which makes him scream, and the chain continues.

Kelsey's has a licensing agreement through early 2011 with CBS Consumer Products for the rights to the theme song from the 1980s sitcom Cheers, which the chain says could lead to " other opportunities " in the future.

Former staff writer Matthew Fleischer says that " as part of the company ’ s ' plug-and-play ' management strategy, editors, writers and ad directors were moved from city to city within the chain, without regard for local knowledge.

One says that relative homology is given by the relative cycles, chains whose boundaries are chains on A, modulo the relative boundaries ( chains that are homologous to a chain on A, i. e. chains that would be boundaries, modulo A again ).

MA ( k ) says that for any partial order satisfying the countable chain condition ( hereafter ccc ) and any family of dense sets in, whose cardinality is at most k, there is a filter on such that ∩ is non-empty for every.

Albert further explains that these constantly diverging paths do sometimes converge again, though as the result of a different chain of causes ; for example, he says, in one possible time-line Dr. Tsun has come to his house as an enemy, in another as a friend.

However, after solving a chain of several of these, he finds a text that says that there will be no more clues and he must solve the rest of the book on his own.

-as he says to Stephen, to have ' A chain right round to the Pacific '.