Definition, Meaning & Synonyms
differentiable
Adjective
/ˌdɪfəˈrɛnʃəbl/
Definition
Capable of being differentiated; having a derivative at a given point or over an interval.
Examples
- The function f(x) = x² is differentiable everywhere on the real number line.
- To be considered differentiable at a point, the limit of the difference quotient must exist.
- In calculus, we often analyze whether a function is differentiable before solving complex integrals.
Meaning
In mathematics, a function is said to be differentiable if it has a derivative at each point in its domain. This means that the function is smooth and does not have any sharp turns or breaks.
Synonyms
- smooth
- derivable
- continuous
