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Calculus. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [1][2][3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules.
In mathematics, the Rayleigh quotient[1] (/ ˈreɪ.li /) for a given complex Hermitian matrix and nonzero vector is defined as: [2][3] For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose to the usual transpose . Note that for any non-zero scalar .
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
For algorithms describing how to calculate the remainder, see division algorithm.) The remainder, as defined above, is called the least positive remainder or simply the remainder . [ 2 ] The integer a is either a multiple of d , or lies in the interval between consecutive multiples of d , namely, q⋅d and ( q + 1) d (for positive q ).
In linear algebra, a quotient space is a vector space formed by taking a quotient group, where the quotient homomorphism is a linear map. By extension, in abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra. However, the use of the term for the more general cases ...
Difference quotient. In single-variable calculus, the difference quotient is usually the name for the expression. which when taken to the limit as h approaches 0 gives the derivative of the function f. [1][2][3][4] The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the ...