differentiable's Usage Examples:

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.

the very minimum, a function could be considered "smooth" if it is differentiable everywhere (hence continuous).

more complex variables that is, at every point of its domain, complex differentiable in a neighborhood of the point.

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow.

One important class of manifolds is the class of differentiable manifolds; this differentiable structure allows calculus to be done on manifolds.

topological curves to distinguish them from more constrained curves such as differentiable curves.

mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.

closed and bounded non-trivial interval of the real line Continuously differentiable ⊂ Lipschitz continuous ⊂ α-Hölder continuous where 0 < α ≤ 1.

point in the domain of the function where the function is either not differentiable or the derivative is equal to zero.

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇ f.

not be differentiable there.

For example, the absolute value function given by f(x) = |x| is continuous at x = 0, but it is not differentiable there.

is differentiable at a point, its differential is given in coordinates by the Jacobian matrix.

However a function does not need to be differentiable for.

[citation needed] As a differentiable function of a complex variable is equal to its Taylor series (that is.

For a piecewise function to be differentiable on a given interval in its domain, the following conditions have to.

example of a real-valued function that is continuous everywhere but differentiable nowhere.

necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.

derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.

topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms.

Synonyms:

distinguishable;

Antonyms:

same; indistinguishable;