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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
Analytic Function. A complex function is said to be analytic on a region if it is complex differentiable at every point in. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with analytic function (Krantz 1999, p. 16). complex function may fail to be analytic at one or more points through the presence of singularities, or along lines or line segments through the presence of branch cuts. A complex function that is analytic at all finite points of the complex plane is said to be entire.