differentiability
- noun
- /ˌdɪfərɛnʃiˈɑːbɪlɪti/
- Specialized
- In calculus, we often discuss differentiability to ensure that we can find the derivative of a function.
Examples
-
So we're going to check differentiability or if they're differentiable.
-
This metric must be "imported" on the differentiable manifold, and for this import, the condition of differentiability must hold.
Academic text (1998) -
Leibniz could accept the differentiability structure on the manifold, since it could flesh out his claim about the adequacy of the perceptual-monadic realm and the ideal realm.
Academic text (1998) -
To determine if a function is smooth, we need to analyze its differentiability at each point.
-
A continuous function has differentiability if it can be derived within its entire domain.
How Smooth
Surface Forms
Morphology
differentiability = differentiable (semi-transparent) = different + iate + able + ity
The noun is a regular nominalization of 'differentiable' with '-ity', so the form and meaning are straightforwardly related.
Etymology
Differentiability comes from different ('not the same') plus -ability ('can be'), via the verb differentiate ('to show a difference'). So differentiability is the idea of 'being able to show small differences', and in maths it means a function 'can have' a derivative so you can measure its small change or slope at a point.