differentiability (Meaning)
differentiability
to discriminate or give expression to a specific difference that distinguishes, to undergo differentiation (see differentiation sense 3b), to cause differentiation in (a specimen for microscopic examination) by staining, to cause differentiation of in the course of development, to become distinct or different in character, to obtain the mathematical derivative (see derivative entry 1 sense 3) of, to make or become different in some way, to mark or show a difference in, to develop differential or distinguishing characteristics in, to recognize or express a difference, to undergo differentiation, to constitute a difference that distinguishes, to recognize or give expression to a difference, to undergo or cause to undergo differentiation in the course of development, to see or state the difference or differences, to express the specific distinguishing quality of, to cause differentiation (see differentiation sense 3b) of in the course of development
Synonyms & Antonyms of differentiability
differentiability Sentence Examples
- Continuous differentiability is a crucial property in calculus for ensuring the smoothness of functions.
- The differentiability of the function allows us to determine its rate of change at any given point.
- The second-order differentiability guarantees that the function has continuous first and second derivatives.
- The lack of differentiability at certain points can indicate discontinuities or other irregularities in the function's behavior.
- The concept of differentiability plays a fundamental role in optimization techniques, such as finding extrema of functions.
- The higher the order of differentiability, the more information we have about the local behavior of the function.
- Piecewise differentiability means that the function can have different smoothness properties over different intervals.
- Differentiability is a necessary condition for the existence of Taylor series expansions, which approximate functions locally.
- In complex analysis, holomorphic functions possess differentiability in the entire complex plane.
- The differentiability of vector-valued functions enables us to study the directional derivatives and gradients, which are useful in vector calculus and differential geometry.
FAQs About the word differentiability
to discriminate or give expression to a specific difference that distinguishes, to undergo differentiation (see differentiation sense 3b), to cause differentiat
modification, dissimilarity, discriminability,distinguishability, diversity, change, contrast, divergence, distinctiveness, deviance
similarity, sameness, agreement, resemblance, likeness, identity, community, analogy, correspondence, parallelism
Continuous differentiability is a crucial property in calculus for ensuring the smoothness of functions.
The differentiability of the function allows us to determine its rate of change at any given point.
The second-order differentiability guarantees that the function has continuous first and second derivatives.
The lack of differentiability at certain points can indicate discontinuities or other irregularities in the function's behavior.
