How Do You Spell DIFFERENTIABLE?

Pronunciation: [dˈɪfəɹˌɛnʃɪəbə͡l] (IPA)

Differentiable is spelled as [ˈdɪfəˌrenʃiəbl] in IPA phonetic transcription. The word refers to a mathematical concept that describes the smoothness or non-discontinuity of a function. The spelling of differentiable reflects the pronunciation of the word, pronounced as "dif-er-en-shi-ə-bəl". The word originates from the Latin word "differentia", meaning "difference" or "distinction". In calculus, the concept of differentiability is crucial for determining the slope of a curve at a given point.

DIFFERENTIABLE Meaning and Definition

1. Differentiable refers to the property of a function or curve to have a derivative at every point within its domain. In mathematics, a function is said to be differentiable if it has a derivative, which represents the rate of change of the function with respect to its independent variable. The derivative of a function at a particular point gives the slope of the tangent line to the graph of the function at that point.

   More precisely, a function f(x) is said to be differentiable at a point x = a if the limit of the difference quotient (f(x) - f(a))/(x - a) exists as x approaches a. This limit is denoted by f'(a) or df/dx|_(x=a) and represents the derivative of f(x) evaluated at x = a.

   If a function is differentiable at every point in its domain, it is called a differentiable function. Such functions are smooth and continuous, and their graphs do not contain any sharp turns or cusps. Differentiability implies continuity, but continuity alone does not guarantee differentiability.

   Differentiability plays a crucial role in calculus, where it allows for the calculation of rates of change, optimization, and other key concepts. It is a fundamental property that characterizes the behavior of functions and their local approximation by linear functions.

Common Misspellings for DIFFERENTIABLE

• sifferentiable
• xifferentiable
• cifferentiable
• fifferentiable
• rifferentiable
• eifferentiable
• dufferentiable
• djfferentiable
• dkfferentiable
• dofferentiable
• d9fferentiable
• d8fferentiable
• didferentiable
• dicferentiable
• divferentiable
• digferentiable
• ditferentiable
• dirferentiable
• difderentiable
• diferentiable
• differntiable
• differentiabel
• differnciable

Etymology of DIFFERENTIABLE

The word "differentiable" in mathematics is derived from the Latin word "differentia", which means "difference" or "distinction". "Differentia" is the noun form of the Latin verb "differre", which means "to differ" or "to carry apart". In mathematics, "differentiable" is used to describe a function that has a derivative at every point in its domain, indicating the existence of a tangent line or slope at each point.

Similar spelling words for DIFFERENTIABLE

• differentia,
• differential,
• deferential,
• difference limen,
• differentiation,
• differently,
• differentiated,
• differentiate,
• differentially,
• differentiator,
• differential gear,
• differential cost.