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Symmetric derivative. In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as: [1] [2] The expression under the limit is sometimes called the symmetric difference quotient. [3] [4] A function is said to be symmetrically differentiable at a point x if its symmetric derivative exists at that ...
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 , .
Quotient space (topology) Illustration of the construction of a topological sphere as the quotient space of a disk, by gluing together to a single point the points (in blue) of the boundary of the disk. In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological ...
Dermatology Life Quality Index. The Dermatology life Quality Index (DLQI) is a ten-question questionnaire used to measure the impact of skin disease on the quality of life of an affected person. It is designed for people aged 16 years and above.
The Rayleigh's quotient represents a quick method to estimate the natural frequency of a multi-degree-of-freedom vibration system, in which the mass and the stiffness matrices are known. The eigenvalue problem for a general system of the form. in absence of damping and external forces reduces to. The previous equation can be written also as the ...
The cokernel of a linear operator T : V → W is defined to be the quotient space W/im(T). Quotient of a Banach space by a subspace. If X is a Banach space and M is a closed subspace of X, then the quotient X/M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section.
In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of ...
A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. [1] In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a ...