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Differentiability is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

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Differentiability in a sentence

Differentiability meaning

  1. The ability to be differentiated.
  2. The existence of the derivative.

Using Differentiability

  • The main meaning on this page is: The ability to be differentiated. | The existence of the derivative.
  • In the example corpus, differentiability often appears in combinations such as: of differentiability, complex differentiability, fréchet differentiability.

Context around Differentiability

  • Average sentence length in these examples: 20.9 words
  • Position in the sentence: 6 start, 2 middle, 6 end
  • Sentence types: 14 statements, 0 questions, 0 exclamations

Often before:

complex 3× real 1× non 1× half 1× preserve 1×

Often after:

implies 1× suppose 1× class 1×

Sentence patterns with Differentiability

These short patterns come directly from the example sentences and show how the word is often embedded:

assumption of differentiability or even 1× by their differentiability class 1× complex differentiability has much 1× complex differentiability suppose that 1× criterion for differentiability 1× definition of differentiability of f 1× definition of differentiability of g 1× ensure complex differentiability at that 1×

Sentence openings and endings

Common sentence openings:

axiomatic approach richard 1× complex differentiability has 1× complex differentiability suppose 1× corollary a simple 1× finally since differentiability 1× fréchet differentiability is 1×

Common sentence endings:

can be shown 1× criterion for differentiability 1× differentiability or continuity 1× hypothesis of differentiability 1× implies non differentiability 1× may be finite 1×

Words around Differentiability

Just before it in the word index:

differentia 7 different 38.746 differencing 9 differencies 2 differences 3.846 differenced 2

Just after it in the word index:

differentiable 74 differential 589 differentially 25 differentials 47 differentiate 438 differentiated 254

Similar in corpus frequency:

aaronson 18 abai 18 abass 18 abatements 18 abdulfatah 18 abebe 18

Corpus analysis for Differentiability

  • In this selection, "differentiability" usually appears near the start of the sentence. The average example has 20.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, complex, real, non, implies, suppose and class stand out and add context to how "differentiability" is used.
  • Recognizable usage signals include assumption of differentiability or even and by their differentiability class. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "differentiability" sits close to words such as aaronson, abai and abass, which helps place it inside the broader word index.

Example types with differentiability

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

One can classify functions by their differentiability class. (8 words)

Fréchet differentiability is a stronger condition than Gâteaux differentiability. (9 words)

Complex differentiability has much stronger consequences than usual (real) differentiability. (10 words)

Longer example sentences

For ψ to be a wavelet for the continuous wavelet transform (see there for exact statement), the mother wavelet must satisfy an admissibility criterion (loosely speaking, a kind of half-differentiability) in order to get a stably invertible transform. (39 words)

The first step is to substitute for g(a + h) using the definition of differentiability of g at a: : The next step is to use the definition of differentiability of f at g(a). (34 words)

Complex differentiability Suppose that : is a function of a complex number z. Then the complex derivative of f at a point z 0 is defined by : provided this limit exists. (30 words)

Example sentences (14)

Complex differentiability has much stronger consequences than usual (real) differentiability.

Finally, since differentiability implies continuity, the contrapositive states discontinuity implies non-differentiability.

Fréchet differentiability is a stronger condition than Gâteaux differentiability.

The first step is to substitute for g(a + h) using the definition of differentiability of g at a: : The next step is to use the definition of differentiability of f at g(a).

The quasi-derivative is another generalization of directional derivative that implies a stronger condition than Gâteaux differentiability, but a weaker condition than Fréchet differentiability.

Axiomatic approach Richard T. Cox showed that Bayesian updating follows from several axioms, including two functional equations and a hypothesis of differentiability.

Complex differentiability Suppose that : is a function of a complex number z. Then the complex derivative of f at a point z 0 is defined by : provided this limit exists.

Corollary A simple but very useful consequence of L'Hopital's rule is a well-known criterion for differentiability.

Advertentie

For ψ to be a wavelet for the continuous wavelet transform (see there for exact statement), the mother wavelet must satisfy an admissibility criterion (loosely speaking, a kind of half-differentiability) in order to get a stably invertible transform.

One can classify functions by their differentiability class.

Relation to differentiability and integrability Every differentiable function : is continuous, as can be shown.

The assumption of differentiability or even continuity is controversial; Halpern found a counterexample based on his observation that the Boolean algebra of statements may be finite.

The sequence with converges pointwise but not uniformly: : In this example one can easily see that pointwise convergence does not preserve differentiability or continuity.

The sole existence of partial derivatives satisfying the Cauchy–Riemann equations is not enough to ensure complex differentiability at that point.

Advertentie

Common combinations with differentiability

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "differentiability" in a sentence?
An example: "Complex differentiability has much stronger consequences than usual (real) differentiability." This page contains 10+ example sentences with the word "differentiability" from authentic English texts.
What does "differentiability" mean?
Differentiability means: The ability to be differentiated.
How many example sentences with "differentiability" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "differentiability", drawn from a database of millions of English sentences.