differentiable function

[/ˌdɪfəˈrenʃəbəl ˈfʌŋkʃən/]
nounfemininepl: differentiable functions / funções diferenciáveis
função diferenciável
1. A mathematical function that has a well-defined derivative at every point in its domain; a function whose graph has a tangent line at each point and does not have any sharp corners or discontinuities
The function f(x) = x² is a differentiable function because its derivative f'(x) = 2x exists at all real numbers.
A função f(x) = x² é uma função diferenciável porque sua derivada f'(x) = 2x existe em todos os números reais.
2. In calculus and mathematical analysis, a function that is smooth and continuous with continuous first derivatives
Differentiable functions are essential in optimization problems and machine learning algorithms.
Funções diferenciáveis são essenciais em problemas de otimização e algoritmos de aprendizado de máquina.
This is a specialized mathematical term used in academic contexts in both Brazil and Portugal. It is fundamental to calculus education in Portuguese-speaking universities and is used identically across regions. The term carries no colloquial variations and maintains consistent usage in mathematical literature, research papers, and educational materials.
Synonyms / Sinônimos
smooth functioncontinuously differentiable functionC¹ function
Antonyms / Antônimos
non-differentiable functiondiscontinuous functionsingular function

Regional Variations

General Brazilian Portuguese
função diferenciável
Standard academic term used in mathematics education and research
Portugal
função diferenciável
Same usage as Brazil; common in Portuguese universities
Academic (International)
função diferenciável
Used consistently across Portuguese-speaking mathematical communities

Related Words

derivativecontinuitycalculustangent linesmoothcontinuously differentiable

Related Idioms & Phrases

differentiable at a point
differentiable on an interval
continuously differentiable
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