- Elasticity of a function
In

mathematics ,**elasticity**of a positivedifferentiable function "f" at point "x" is defined as:$Ef(x)\; =\; frac\{x\}\{f(x)\}f\text{'}(x)\; =\; frac\{d\; log\; f(x)\}\{d\; log\; x\}$It is the ratio of the incremental change of the logarithm of a function with respect to an incremental change of the logarithm of the argument. This definition of elasticity is also called**point elasticity**, and is the limit ofarc elasticity between two points.The term elasticity is widely used in

economics ; seeelasticity (economics) for details.**Rules**Let "a" be a constant. Then:$E\; a\; =\; 0$, :$E\; a\; f(x)\; =\; a\; E\; f(x)$, and:$E\; x^a\; =\; a.$Any function f has constant point elasticity if and only if it is a monomial of the form $ax^b$.

Although elasticity is not a

linear operator like the derivative, rules for finding the elasticity of products and quotients are simpler than those for derivatives. Let "f, g" be differentiable. Then:$E\; f(x)\; cdot\; g(x)\; =\; E\; f(x)\; +\; E\; g(x).$:$E\; frac\{f(x)\}\{g(x)\}\; =\; E\; f(x)\; -\; E\; g(x).$:$E\; (f\; circ\; g)(x)\; =\; E\; f(g(x))\; cdot\; E\; g(x).$The differentiation can be expressed in terms of elasticity as:$D\; f(x)\; =\; frac\{E\; f(x)\; cdot\; f(x)\}\{x\}$

**References*** Yves Nievergelt, The Concept of Elasticity in Economics, "SIAM Review", Vol. 25, No. 2 (Apr., 1983), pp. 261-265

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