differentiable

Thân thiện

The biologist carefully notes the differentiable characteristics of the two leaf samples.

Definition

1. Adjective:
   • Capable of being perceived as different: Describes something that can be distinguished or recognized as distinct from something else.
   • Possessing a differential coefficient or derivative: In mathematics, describes a function whose derivative exists at a given point or over an interval.

Usage Examples

• Adjective (General):

  • The two species are differentiable by their distinct markings. (The two species can be told apart by their distinct markings.)
  • The subtle differences in their accents are barely differentiable to a non-native speaker. (The subtle differences in their accents are hardly distinguishable to a non-native speaker.)

• Adjective (Mathematics):

  • The function f(x) = x² is differentiable everywhere. (The function f(x) = x² has a derivative at every point.)
  • To find the slope, ensure the curve is differentiable at that point. (To find the slope, make sure the curve has a derivative at that point.)

Advanced Usage

• "Continuously differentiable": A function that has a derivative which is itself a continuous function.

  • For the solution to be smooth, the function must be continuously differentiable. (For the solution to be smooth, the function must have a continuous derivative.)

• "Nowhere differentiable": A function that does not have a derivative at any point in its domain.

  • The Weierstrass function is a classic example of a continuous but nowhere differentiable function. (The Weierstrass function is a classic example of a function that is continuous but has no derivative at any point.)

Variants and Related Words

• Differentiate (verb): To recognize or ascertain what makes something different; to calculate the derivative of a function.

  • It is important to differentiate between facts and opinions. (It is important to tell the difference between facts and opinions.)
  • You must learn to differentiate polynomial functions. (You must learn to find the derivatives of polynomial functions.)

• Differentiability (noun): The property or condition of being differentiable.

  • The differentiability of the function at the origin is in question. (The existence of the function's derivative at the origin is in question.)

Synonyms

• Distinguishable: Able to be recognized as different.
• Derivable: Capable of having a derivative found (mathematical context).

Antonyms

• Indistinguishable: Not able to be perceived as different.
• Non-differentiable: Lacking a derivative (mathematical context).

Học thuật

Adjective

1. capable of being perceived as different
   • differentiable species
2. possessing a differential coefficient or derivative