In mathematics, elasticity of a differentiable function $f(x)$ at point $x$ is defined as

$E(x)\; =\; \backslash frac\{x\; f\text{'}(x)\}\{f(x)\}\; =\; \backslash frac\{d\; \backslash ln\; f(x)\}\{d\; \backslash ln\; x\}$

It's the ratio of the incremental percentage change of the function with respect to an incremental percentage change of the argument. This definition of elasticity is also called point elasticity. If the function is not differentiable the notion of arc elasticity may apply.

If the elasticity is constant $E(x)\; =\; \backslash alpha$, then the function has a form $f(x)\; =\; C\; x\; ^\; \backslash alpha$ for a constant $C$, which is a solution to the first order differential equation.

The term elasticity has been widely used in economics; see elasticity (economics) for details.

---

Mathematical analysis