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:

Applying this rule of thumb, one can apply " common sense " when creating the duration of a single activity or group of activities necessary to produce a deliverable defined by the WBS.

Applying the induction rule repeatedly, starting from the independently proved base case, proves many, often infinitely many, other cases.

Applying the term to the work of Philip Pullman ( His Dark Materials ), Schweizer clarifies that he does not mean the term to carry the negative connotations of misanthropy: " To me, the word connotes a heroic stance of humanistic affirmation and the courage to defy the powers that rule the universe.

Applying the product rule for differentiation to d ( TS )

Applying this rule often adds humor for both players and on-lookers.

Applying the rule of epoché one sets aside one's initial biases and prejudices in order to suspend expectations and assumptions.

Applying the rule of horizontalization one treats each item of description as having equal value or significance.

Applying the chain rule and first order condition,

Applying his originalist understanding of the Ex Post Facto Clause, Justice Scalia concluded that the Tennessee Supreme Court's retroactive application of its decision to remove the year-and-a-day rule from its jurisprudence rendered Rogers's conviction for murder invalid.

* Applying this rule, the Ninth Circuit nevertheless concluded — in agreement with the district court --

Applying the product rule to the left hand side of ( 3 ) and equating to the left hand side of ( 2 )

Applying an ancient rule that when a husband and wife are known to be alone together behind a closed door the law presumes sexual intercourse may well have taken place, Rabbi Yosef concluded that it was possible the former husband was the daughter's father and hence Jewish law, which very strongly construes all evidence in favour of birth within marriage, had to presume that he was.

Applying the modern rule, both titles descend to heirs general, which left them in abeyance between the daughters of Sir Owen West, and this situation persists to the present day with their respective heirs.

Applying the principle of indirect rule, the British allowed native authorities to administer populations according to their own traditions.

Applying a false trade description to goods is a strict liability offence: provided it is shown that the description was applied and was false, the accused has to prove certain defences in order to escape conviction.

Applying Fubini's theorem and integrating on the fiber, one gets

Applying the variational principle to the base metric g, one gets the Einstein equations

Applying Gram-Schmidt one obtains an orthonormal basis for.

Applying the inverse-square law between the charges on the electron and nucleus, one can write:

Applying ROT13 to a piece of text merely requires examining its alphabetic characters and replacing each one by the letter 13 places further along in the alphabet, wrapping back to the beginning if necessary.

Applying a rotation means here rotating one of the two rods 360 degrees.

Applying thick wraps to both of his knees became a pre-game ritual, and by the end of his career, simply swinging a bat caused him to fall to one knee in pain.

Applying power to one cathode surrounds it with an orange glow discharge.

Applying this to a space of dimension 0, which contains exactly one vector ( the zero vector ), the only candidate for a basis is the empty set ( both because 0 elements are required, and because the zero vector cannot be in any basis ).

Applying this model to the experiences of Mexican Americans forces one to see Mexican American immigrants as positive additions to the " American melting pot ," in which as more additions are made to the pot, the more equal and accepting society will become.

Applying for a commercial pilot's licence on 2 June 1921 ( in which he gave his name as ' Charles Edward Kingsford-Smith '), he became one of Australia's first airline pilots when he was chosen by Norman Brearley to fly for the newly formed West Australian Airways.

Applying this procedure to the structure sheaf, one recovers the Hilbert polynomial of X.

Applying these relations to the strings above, one obtains

Applying the Tannakian formalism, one concludes that M < sub > num </ sub > is equivalent to the category of representations of an algebraic group G, which is called motivic Galois group.

# Applying for a licence: Currently only one type of licence is available to new applicants, the possession-acquisition licence ( PAL ).

Applying this concept to human society, Kropotkin presented mutual aid as one of the dominant factors of evolution, the other being self assertion, and concluded that In the practice of mutual aid, which we can retrace to the earliest beginnings of evolution, we thus find the positive and undoubted origin of our ethical conceptions ; and we can affirm that in the ethical progress of man, mutual support not mutual struggle – has had the leading part.

Applying Itō's lemma to the process one gets

Applying the Nernst Equation above, one may account for these differences by changes in relative K < sup >+</ sup > concentration or differences in temperature.

Applying the most commonly cited definition of systemic risk, that of the Financial Stability Board ( FSB ), to the core activities of insurers and reinsurers, the report concludes that none are systemically relevant for at least one of the following reasons:

Applying one of these two processes, short-term redundancy ( positive correlation of nearby values ) of the signal is eliminated ; compression ratios on the order of 2 to 4 can be achieved if differences are subsequently entropy coded, because the entropy of the difference signal is much smaller than that of the original discrete signal treated as independent samples.

Applying a result of MacIntyre on the model theory of p-adic integers, one deduces again that ζ < sub > G </ sub >( s ) is a rational function in p < sup >− s </ sup >.

Applying Lagrange's formula with the observation that Ω • r ( t ) = 0 at all times,

Applying higher pressure of the order of hundreds or thousands of kilobars induces a series of phase transformations, in particular with a tetragonal phase appearing at about 900 kbar.

Applying Chow's analysis to the case of the unexpected hanging ( again with the week shortened to two days for simplicity ), we start with the observation that the judge's announcement seems to affirm three things:

Applying a conception of such illocutionary acts according to which they are ( roughly ) acts of saying something with the intention of communicating with an audience, he describes indirect speech acts as follows: " In indirect speech acts the speaker communicates to the hearer more than he actually says by way of relying on their mutually shared background information, both linguistic and nonlinguistic, together with the general powers of rationality and inference on the part of the hearer.

Applying the rules and customs of prize law, the courts decided whether the Letter of Marque was valid and current, and whether the captured vessel or its cargo in fact belonged to the enemy ( not always easy, when flying false flags was common practice ), and if so the prize and its cargo were " condemned ", to be sold at auction with the proceeds divided among the privateer's owner and crew.

Applying a pulse with specified width and voltages to the spades made the sheet advance to the next anode, where it stayed until the next advance pulse.

* Greening The Desert: Applying natural farming techniques in Africa, interview with Masanobu Fukuoka ( retrieved 30 November 2010 )

Applying this recursively gives an algorithm with a multiplicative cost of.

The Cholesky decomposition is commonly used in the Monte Carlo method for simulating systems with multiple correlated variables: The correlation matrix is decomposed, to give the lower-triangular L. Applying this to a vector of uncorrelated samples, u, produces a sample vector Lu with the covariance properties of the system being modeled.

Applying Itō's lemma with f ( S ) =

Applying Itō's lemma with f ( Y ) = log ( Y ) gives

Applying to the French classics the rigorous method used with regard to the texts of the Middle Ages, he published the Pensées of Pascal, revised with the original manuscript ( 1887 – 1889 ), and the Provinciales ( 1891 ), edited with notes.

Applying this with, then and

Applying procedural fairness to an entire society therefore seems certain to create recognizable inefficiencies, and therefore be unfair, and ( by the equivalence of justice with fairness ) unjust.

Applying again Bayes ' theorem, and assuming the classification between spam and ham of the emails containing a given word (" replica ") is a random variable with beta distribution, some programs decide to use a corrected probability:

Applying these methods in the workplace, such as Csikszentmihalyi did with Swedish police officers, can improve morale by fostering a sense of greater happiness and accomplishment, and in correlated to increased performance.

Applying the chaos theory to the second law of thermodynamics, the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations.