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Differentiable function
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
Weierstrass function
continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass. Historically, the Weierstrass function is important because
Smoothness
complex function is differentiable just once on an open set, it is both infinitely differentiable and analytic on that set. Smooth functions with given
Holomorphic function
just differentiable at z0, but differentiable everywhere within some neighbourhood of z0 in the complex plane. Given a complex-valued function f of a
Differentiable manifold
another is differentiable), then computations done in one chart are valid in any other differentiable chart. In formal terms, a differentiable manifold
Differentiation of trigonometric functions
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change
Non-analytic smooth function
mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily
Implicit function theorem
are differentiable, and it even works in situations where we do not have a formula for f(x, y). Let f : Rn+m → Rm be a continuously differentiable function
Analytic function
some ways, but different in others. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold
Convex function
that interval. If a function is differentiable and convex then it is also continuously differentiable. A differentiable function of one variable is convex