In the Lagrangian description, the material derivative of is simply the partial derivative with respect to time, and the position vector is held constant as it does not change with time.

Recall that when the total derivative exists, the partial derivative in the ith coordinate direction is found by multiplying the Jacobian matrix by the ith basis vector.

The present IUPAC definition is that affinity A is the negative partial derivative of Gibbs free energy G with respect to extent of reaction ξ at constant pressure and temperature.

: denotes the partial derivative of with respect to evaluated for

: denotes the partial derivative of with respect to evaluated for.

One way of expressing the Lie bracket is through the formalism of Lie derivatives, which identifies a vector field X with a first order partial differential operator L < sub > X </ sub > acting on smooth functions by letting L < sub > X </ sub >( f ) be the directional derivative of the function f in the direction of X.

where u < sub > x </ sub > is the first partial derivative of u with respect to x.

Some partial derivative approximations are:

Maximizing the log-likelihood first requires taking the partial derivative with respect to β:

where is the partial derivative of with respect to its first argument, evaluated at.

Taking the best linear approximation in a single direction determines a partial derivative, which is usually denoted ∂ y /∂ x.

The second derivative test can still be used to analyse critical points by considering the eigenvalues of the Hessian matrix of second partial derivatives of the function at the critical point.

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant ( as opposed to the total derivative, in which all variables are allowed to vary ).

The partial derivative of a function f with respect to the variable x is variously denoted by

The modern partial derivative notation is by Adrien-Marie Legendre ( 1786 ), though he later abandoned it ; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841.

That is, the partial derivative of z with respect to x at is 3.

This is the partial derivative of f with respect to y.

Here ∂ is a rounded d called the partial derivative symbol.

In general, the partial derivative of a function f ( x < sub > 1 </ sub >,..., x < sub > n </ sub >) in the direction x < sub > i </ sub > at the point ( a < sub > 1 </ sub >,..., a < sub > n </ sub >) is defined to be:

In this case f has a partial derivative ∂ f /∂ x < sub > j </ sub > with respect to each variable x < sub > j </ sub >.

One of the first known uses of the symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences.

The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings — gradient, divergence, and curl — can be formally viewed as the product of scalars, dot product, and cross product, respectively, of the del " operator " with the field.

p ' ye-baek – pacte civil de solidarité – pain during intercourse – painful ejaculation – painful intercourse – painful ovulation – painful sex – pair-bonding – pairbond – pait likkhi – panderer – pandering – pansexual – pansexuality – panty fetishism – panty liner – panty pad – pantyhose fetishism – para 0 – para 1 – paramesonephric ducts – paranymph – paraphilia – paraphiliac – paraphilic adolescentilism – paraphilic gerontalism – paraphilic infantilism – paraphilic juvenilism – paraphimosis – parasympathetic nervous system – paraurethral glands – parovarium – paroöphoron – Parsee wedding – Parsi marriage customs – Parsi wedding – parthenogenesis – parthenos – partial androgen insensitivity syndrome – partialism – partialism ( paraphilia ) – partible paternity – party and play – passivism – pasties-paternity – paternity suit – pathicus – patriarchy – patrilocal residence – pearling – pearly penile papules – pecattiphilia – pedal pumping – pederasty – pediophilia – pedophilia – 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plaçage – plethysmography – plural marriage – plushophile – plushophilia – PnP – podophilia – point of no return – polyamory – polyandry – polyandry in Tibet – polycystic ovary syndrome – polyfidelity – polygamy – polygynandry – polygyny – polyiterophilia – polymastia – polymorphous perverse – polymorphous perversity – polythelia – pomosexual – pompoir – pony boots ( fetish footwear ) – ponyboy – ponygirl – poppers – popping her cherry – population control – Pornographic film actor – pornai – pornographic magazine – pornographic movie – pornographic novel – pornography – pornography in Europe – pornography in Japan – pornography in the United States – post-coital tristesse – post-natal depression – post-orgasmic pain – post-partum sex taboo – posterior commissure of labia – posthumous marriage – postmasturbatory urine – postpartum examination – potency – pozcum – pre-eclampsia – pre-ejaculate – pre-ejaculatory fluid – pre-marital sex – pre-menstrual tension – pre-op transsexual – precocious puberty – predicament bondage – prednisone – pregnancy – pregnancy fetishism – pregnancy over age 50 – Prehn's sign – preimplantation genetic diagnosis – premarital intercourse – premature ejaculation – premature puberty – premenstrual dysphoric disorder – premenstrual stress syndrome – prenatal masculinization – prenatal screening – prenatal testing – prenuptial agreement – prepenetrative orgasm – prepuce ( disambiguation ) – prepuce plasty – preputial plasty – preputial ring – preputial stenosis – preputioplasty – President's Commission on Obscenity and Pornography – priapism – Priapus – primatologist – primigravida – Prince Albert piercing – prince's wand – Princess Albertina – prison rape – prison sexuality – private dancer-proceptive phase – procurer – professional dominant – professional dominatrix – professional submissive – progesterone – progesterone only pill – progestin – progestin-induced hermaphroditism – progestin-induced virilisation – progestogen – prohibited degree of kinship – prolactin – prolactin-inhibitory factor – promiscuity – prophylactic – prostaglandins – prostate – prostate cancer – prostate massage – prostate milking – prostate orgasm – prostate specific antigen – prostate-specific antigen – prostatectomy – prostatic congestion – prostatic ducts – prostatic sinus – prostatic urethra – prostatic utricle – prostatitis – prosthesis – prosthetic testis – prosthetics – prostitute – prostitute's maid – prostitutes ' maid – prostitution – prostitution in Africa – prostitution in ancient Egypt – prostitution in ancient Greece – prostitution in ancient Rome – prostitution in Asia – prostitution in Australia – prostitution in Austria – prostitution in Canada – prostitution in China – prostitution in Denmark – prostitution in Europe – prostitution in Finland – prostitution in France – prostitution in Germany – prostitution in Hong Kong – prostitution in Iceland – prostitution in India – prostitution in Italy – prostitution in Japan – 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** ∂, the partial derivative symbol, often read as " partial "

Pownall was opposed to Prime Minister North's partial repeal in 1770 of the hated Townshend Acts, which maintained the tax on tea as a symbol of Parliamentary power.

This features the word " at " surrounded by a partial circle, reminiscent of an @ symbol.

As a shorthand notation, the nabla symbol and the partial derivative symbols are frequently dropped, and instead a semi-colon and a comma are used to set off the index that is being used for the derivative.

An angry mob then set fire to the Palace of Justice ( Justizpalast ), seen as a symbol of a flawed and partial judicial system.

Again, further in terms of thermodynamics, the internal energy of the calorimetric material can sometimes, depending on the calorimetric material, be considered as the value of a function of, with partial derivatives and, and with being expressible as the value of a function of, with partial derivatives and.

Localization-related epilepsies, sometimes termed partial or focal epilepsies, arise from an epileptic focus, a small portion of the brain that serves as the irritant driving the epileptic response.

Authorities emphasize different seizure types as important in LGS, but most have astatic seizures ( drop attacks ), tonic seizures, tonic-clonic seizures, atypical absence seizures, and sometimes, complex partial seizures.

Most of these patients have complex partial seizures sometimes preceded by an aura, and some TLE patients also suffer from secondary generalized tonic-clonic seizures.

In a system built from separates, sometimes a failure on one component still allows partial use of the rest of the system.

Local anesthetic injections into the nerves or sensitive areas of the stump may relieve pain for days, weeks or, sometimes permanently, despite the drug wearing off in a matter of hours ; and small injections of hypertonic saline into the soft tissue between vertebrae produces local pain that radiates into the phantom limb for ten minutes or so and may be followed by hours, weeks or even longer of partial or total relief from phantom pain.

Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call " vacuum " or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space.

Vector calculus ( or vector analysis ) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space The term " vector calculus " is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.

This apparatus is sometimes confused with the Crookes radiometer of 1873, in which vanes turn in a partial vacuum under the influence of low pressure gas molecules and not directly by the photons themselves.

A related result, sometimes called the second Borel – Cantelli lemma, is a partial converse of the first Borel – Cantelli lemma.

To distinguish it from the letter d, ∂ is sometimes pronounced " del " or " partial " instead of " dee ".

( This essentially simulates an infinite periodic tiling, and in the field of partial differential equations is sometimes referred to as periodic boundary conditions.

When sufficiently large, the nodules compress the urethral canal to cause partial, or sometimes virtually complete, obstruction of the urethra, which interferes with the normal flow of urine.

Thrombocytopenia is sometimes extreme, with alteration in prothrombin time ( PT ) and partial thromboplastin time ( PTT ) suggestive of diffuse intravascular coagulation ( DIC ).

The shaving of head hair is also sometimes done by cancer patients when their treatment may result in partial hair loss.

Many indigenous people, and sometimes those with partial African descent, were classified as mestizo if they spoke Spanish and lived as mestizos.

The gooseberry in the south of England will grow well in cool situations, and may be sometimes seen in gardens near London flourishing under the partial shade of apple trees ; but in the north it needs full exposure to the sun to bring the fruit to perfection.

Government-owned or state-run enterprises are often the result of corporatization, a process in which government agencies and departments are re-organized as semi-autonomous corporate entities, sometimes with partial shares listed on stock exchanges.

As partial compensation, " Ekstra Bladet " launched a website where the Page 9 Girls could choose to make a gallery for, and on this site ( which is a pay-site ) sometimes the model is fully nude, but it is rare.

Among the most notable were the historians Herodotus ( 484 – 425 ), who described the Greco-Persian Wars ; Thucydides ( 460 – 395 ), who wrote the great History of the Peloponnesian War ; and Xenophon ( 427 – 335 ), who, although sometimes considered a partial and poorly documented writer, in the opinion of historians left a useful source of information about the first years of the 4th century BC.

This notation, common in pre-Classical music, is sometimes known as a partial key-signature.

A particular problem when using a closed circuit rebreather is the drop in ambient pressure caused by the ascent phase of the dive, which reduces the partial pressure of oxygen to hypoxic levels leading to what is sometimes called deep water blackout.

In addition to the " partial " characters mentioned above, the two-silk-text-characters sometimes use characters that are different from the ones present in the texts that have come down to us through consecutive publications of the later version of the ' named work '.