differentiable

Meanings

• adjective

  A function that can be represented by a curve that can be drawn without lifting the pen from the paper.

  - "The function f(x) = x^2 is differentiable at every point in its domain."
  - "Since the derivative of a differentiable function exists at every point, we can use it to find the function's instantaneous rate of change."

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Variants

List of all variants of differentiable that leads to same result
differentiabilities , differentiability , differentiable , differentiate , differentiated , differentiates , differentiating

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Etymology

origin and the way in which meanings have changed throughout history.

The term 'differentiable' comes from the Latin word 'differens,' meaning 'different,' and the suffix 'able,' meaning 'capable of.'

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The term 'differentiable' was first introduced by German mathematician Gottfried Wilhelm Leibniz in the late 17th century.

2. Differentiable functions have many important properties, such as being able to be integrated and having inverse functions.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Derivative: The derivative of a differentiable function at a given point is the slope of the tangent line to the function at that point.

2. Calculus: Differentiability is a key concept in calculus, which deals with the study of functions and their rates of change.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

The concept of differentiability is fundamental in mathematics and physics, and has applications in various fields such as engineering, economics, and computer science.

How to Memorize "differentiable"

1. visualize
   

   - To visualize a differentiable function, imagine a curve that can be drawn smoothly without lifting the pen from the paper.
   - Think of a rubber band that can be stretched and bent smoothly without breaking.

2. associate
   

   - Associate the word 'differentiable' with the idea of a function that can be drawn as a smooth curve.
   - Think of the word 'smoothly' or 'continuously' when you encounter the term 'differentiable'.

3. mnemonics
   

   - Try creating a mnemonic like 'Different functions are always differentiable, just like a smooth rabbit in a differentiable harem.'

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