continuous function; there exist functions that are differentiable but not continuously differentiable (an example is given in the section Differentiability classes)...

differentiable functions. If a complex function is differentiable just once on an open set, it is both infinitely differentiable and analytic on that set [citation...

mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily...

(see the figure), piecewise continuous functions, and piecewise differentiable functions. Piecewise functions can be defined using the common functional...

of the differentiability of the Riemann function. As the Riemann function is differentiable only on a null set of points, it is differentiable almost...

just differentiable at z0, but differentiable everywhere within some neighbourhood of z0 in the complex plane. Given a complex-valued function f of a...

the inverse function theorem for complex holomorphic functions, for differentiable maps between manifolds, for differentiable functions between Banach...

that interval. If a function is differentiable and convex then it is also continuously differentiable. A differentiable function of one variable is convex...

and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally...

Allendoerfer, Carl B. (1974). "Theorems about Differentiable Functions". Calculus of Several Variables and Differentiable Manifolds. New York: Macmillan. pp. 54–88...