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In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation,
Dysprosium is the chemical element with the symbol Dy and atomic number 66. It is a rare-earth element in the lanthanide series with a metallic silver luster. Dysprosium is never found in nature as a free element, though, like other lanthanides, it is found in various minerals, such as xenotime. Naturally occurring dysprosium is composed of seven isotopes, the most abundant of which is 164Dy.
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of is denoted as , where if and only if , then the inverse function rule is, in Lagrange's notation,
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem.
In mathematics, an implicit equation is a relation of the form where R is a function of several variables. For example, the implicit equation of the unit circle is
In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively.
Dysprosium(III) chloride (DyCl3), also known as dysprosium trichloride, is a compound of dysprosium and chlorine. It is a white to yellow solid which rapidly absorbs water on exposure to moist air to form a hexahydrate, DyCl3·6H2O. Simple rapid heating of the hydrate causes partial hydrolysis to an oxychloride, DyOCl.
Naturally occurring erbium (68Er) is composed of 6 stable isotopes, with 166Er being the most abundant. 39 radioisotopes have been characterized with between 74 and 112 neutrons, or 142 to 180 nucleons, with the most stable being 169Er with a half-life of 9.4 days, 172Er with a half-life of 49.3 hours, 160Er with a half-life of 28.58 hours, 165Er with a half-life of 10.36 hours, and 171Er with a half-life of 7.516 hours. All of the remaining radioactive isotopes have half-lives that are less than 3.5 hours, and the majority of these have half-lives that are less than 4 minutes. This element also has numerous meta states, with the most stable being 167mEr.
Naturally occurring dysprosium (66Dy) is composed of 7 stable isotopes, 156Dy, 158Dy, 160Dy, 161Dy, 162Dy, 163Dy and 164Dy, with 164Dy being the most abundant. Twenty-nine radioisotopes have been characterized, with the most stable being 154Dy with a half-life of 3.0 million years, 159Dy with a half-life of 144.4 days, and 166Dy with a half-life of 81.6 hours. All of the remaining radioactive isotopes have half-lives that are less than 10 hours, and the majority of these have half-lives that are less than 30 seconds. This element also has 12 meta states, with the most stable being 165mDy, 147mDy and 145mDy.
In mathematics, a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in are called double integrals, and integrals of a function of three variables over a region in are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
Superintendent of Police, also known as Deputy Commissioner in Police Department is a senior rank in the Indian Police Service (IPS). They wear a star and an Ashoka emblem on their epaulettes with 'IPS' below. The larger and more important districts in India are headed by a senior superintendent of police (SSP), while smaller district are headed by a superintendent of police (SP).
The DY Patil Stadium,, is a multi-purpose sports stadium in D.Y. Patil sports academy at Nerul in Navi Mumbai, Maharashtra, India.
Tripura Police is the law enforcement agency of the state of Tripura which organizes and is responsible for policing activities in the state of Tripura, Northeast India. It was formed in the year 1965. Currently V.S. Yadav, IPS is DGP of Tripura.
Dysprosium oxide (Dy2O3) is a sesquioxide compound of the rare earth metal dysprosium. It is a pastel yellowish-greenish, slightly hygroscopic powder having specialized uses in ceramics, glass, phosphors, lasers, as a Faraday rotator and dysprosium metal halide lamps.
DY Persei is a variable star and carbon star in the Perseus constellation. At maximum it is 11th magnitude and at its faintest it drops to 16th magnitude. DY Persei is the prototype of the very rare DY Persei class of variables that pulsate like red variables but also fade from sight like R Coronae Borealis variables.
In calculus, interchange of the order of integration is a methodology that transforms iterated integrals of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed. In some cases, the order of integration can be validly interchanged; in others it cannot.
In calculus, the differential represents the principal part of the change in a function with respect to changes in the independent variable. The differential is defined by
Jason James Desiata Dy is a Filipino singer, songwriter, actor and musician. He is best known as the winner of the second season of The Voice of the Philippines.
DY Centauri is a variable star in the constellation Centaurus. From its brightness, it is estimated to be 7000 parsecs (23000 light-years) away from Earth.
Dysprosium(III) fluoride is an inorganic compound of dysprosium with a chemical formula DyF3.
References
- ↑ Land Registry ref DY401396, DY 401522 and Registered Charity 216960
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