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Here, the substitution function (v 1,...,v n) = φ(u 1, ..., u n) needs to be injective and continuously differentiable, and the differentials transform as: = | (, …,) |, where det(Dφ)(u 1, ..., u n) denotes the determinant of the Jacobian matrix of partial derivatives of φ at the point (u 1, ..., u n). This formula expresses the fact that ...
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With the end of colonialism in the 20th century, the resident minister system came to an end, and was replaced by country-to-country diplomatic relations. Legal: 18: 20: Resin worker: Resin workers' work involved the extraction or working of resin, [186] which was needed as a raw material in the manufacture of pitch, tar and turpentine.
If y is a function of x, then the differential dy of y is related to dx by the formula =, where dy/dx denotes the derivative of y with respect to x. This formula summarizes the intuitive idea that the derivative of y with respect to x is the limit of the ratio of differences Δy/Δx as Δx becomes infinitesimal.
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The solutions in terms of the original variable are obtained by substituting x 3 back in for u, which gives x 3 = 1 and x 3 = 8. {\displaystyle x^{3}=1\quad {\text{and}}\quad x^{3}=8.} Then, assuming that one is interested only in real solutions, the solutions of the original equation are
This list contains acronyms, initialisms, and pseudo-blends that begin with the letter Y. For the purposes of this list: acronym = an abbreviation pronounced as if it were a word, e.g., SARS = severe acute respiratory syndrome , pronounced to rhyme with cars
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