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 satisficing to research is a way for researchers to adjust to the vast amount of information today.

Applying mineral oil simply darkens the appearance of the stone ; it does not protect it in any way.

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 this theorem when R is itself a PID gives us a way of building Dedekind domains out of PIDs.

Applying an operation on a scene graph requires some way of dispatching an operation based on a node's type.

Applying separation of variables again to the second equation gives way to the pair of differential equations

Applying this same sensibility to photography, Alfred Stieglitz later stated it this way: " Atmosphere is the medium through which we see all things.

Applying fire to an ecosystem may create habitats for species that have been negatively impacted by fire suppression, or fire may be used as a way of controlling invasive species without resorting to herbicides or pesticides.

Applying cyanoacrylate to some materials made of cotton or wool ( such as cotton swabs, cotton balls, and certain yarns or fabrics ) results in a powerful, rapid exothermic reaction.

Applying to the study of the French Revolution the rules of historical criticism which had produced such rich results in the study of ancient and medieval history, he devoted himself to profound research in the archives, and to the publication of numerous important contributions to the political, administrative and moral history of that period.

Applying such genetic improvement program to aquaculture species will increase productivity to meet the increasing demands of growing populations.

Applying the axiom of choice again we get a function from the first order formulas to such functions

Applying this method, George concluded that many of the problems that beset society, such as poverty, inequality, and economic booms and busts, could be attributed to the private ownership of the necessary resource, land.

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 this result repeatedly shows that there is a basis for V such that all elements of the Lie algebra are represented by upper triangular matrices.

Applying this common law action to computer networks, plaintiffs must first prove that they received some type of electronic communication ( typically bulk e-mail or spam ) that the defendant intentionally sent to interfere with the plaintiff's interest in his or her property and second that this communication caused a quantifiable harm to their tangible property, such as impaired functioning of the computer, network or server.

Applying a CE mark without such certification is a criminal offence.

Applying such preference based approaches has been criticised as a means of deriving the value of ecosystems and biodiversity and for avoiding deliberation, justification and judgment in making choices.

Applying for a credit card requires the applicant to present some proof of regular income ( such as an employment certificate ) or financial assets invested elsewhere.

Applying a business model learned from her former boss, Tom McNeill, she began hiring young women and training them in the wild routine, which included such antics as chugging alcohol, setting light to it, then breathing fire.

Applying multiple, successive gaussian blurs to an image has the same effect as applying a single, larger gaussian blur, whose radius is the square root of the sum of the squares of the blur radii that were actually applied.

Applying Leibniz's Law to the Ship of Theseus problem, S2 is the same as S1 if, and only if, S2 and S1 have all the same properties and relations.

Applying only classical physics and the Bohr model of the atom makes both atomic and molecular ionization entirely deterministic ; that is, every problem will always have a definite and computable answer.

Applying a delta-v at the LEO of only 0. 78 km / s more ( 3. 20-2. 42 ) would give the rocket the escape speed, while at the geostationary orbit a delta-v of 1. 46 km / s is needed for reaching the escape speed of this circular orbit.

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 duality, this means that a morphism in some category C is a monomorphism if and only if the reverse morphism in the opposite category C < sup > op </ sup > is an epimorphism.

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

Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field.

Applying the doctrine of judicial immunity adopted by the U. S. Supreme Court in Bradley v. Fisher in 1871 and held applicable to § 1983 actions in Pierson v. Ray in 1967, Judge Luther M. Swygert, writing for himself and Judges Harlington Wood, Jr., and William G. East, found that immunity is available only when a judge has jurisdiction over the subject-matter of a case and that it is not available when he acts in " clear absence of all jurisdiction.

Applying the techniques developed at Harvard for generating a paradigm from a representative form and its classification, we can add all forms of a word to the dictionary at once.

* D. Young Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems, John Wiley & Sons ( 2001 ).

Applying video compression algorithms like MPEG1, MPEG2 or MPEG4 allows for fractional BPP values.

* 1887 – Herman Hollerith applies for US patent # 395, 791 for the ' Art of Applying Statistics ' – his punched card calculator.

* 1889 – Herman Hollerith is issued US patent # 395, 791 for the ' Art of Applying Statistics ' — his punched card calculator.

Applying ice for 5 minutes to the muscles reportedly has a sensitivity and specificity of 76. 9 % and 98. 3 %, respectively, for the identification of MG.

Applying Gram-Schmidt one obtains an orthonormal basis for.

Applying the first three of the five focusing steps of TOC, the system constraint for all projects is identified as are the resources.

Applying the rational root theorem thus yields the following possible roots for t:

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 the transmission line model based on the telegrapher's equations, the general expression for the characteristic impedance of a transmission line is:

Applying Gibbs free energy equation for reactions:

Applying for a COL does not commit the utilities to construct the plant, but it is part of the licensing process, say officials of all the utilities.

Applying black patch to Barbara Loden's head for hole in head illusion ( 1957 )

Applying himself to this problem, Giacconi worked on the instrumentation for X-ray astronomy ; from rocket-borne detectors in the late 1950s and early 1960s, to Uhuru, the first orbiting X-ray astronomy satellite, in the 1970s.

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 these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v ; the use of the scalar Laplacian and vector Laplacian gives two more:

" Applying Case-Based Reasoning: Techniques for Enterprise Systems ".

Applying the principles of comparative negligence, the jury found that McDonald's was 80 % responsible for the incident and Liebeck was 20 % at fault.