# Derivative

## Noun

**Definition:** Something that is derived from something else; a product, idea, or concept that is based on or derived from another source.

**Definition:** In mathematics, the derivative represents the rate at which a function changes at any given point.

**Synonyms:** Derivative product, Byproduct, Offshoot

**Antonyms:** Original, Primary, Source

**Examples:**

- His painting is a derivative of Picasso's style.
- The derivative of f(x) with respect to x is denoted as f'(x).

**Mnemonics:**

- Think of a derivative as something that is derived from another origin or source.
- In mathematics, the derivative measures how a function is derived or changes.

## Etymology:

**Origin:**

Late Middle English from late Latin 'derivativus', from Latin 'derivare' meaning 'to derive'.

**Historical Usage:**

The word derivative originated in the late Middle English period and has been used in both general English and mathematical contexts since then.

## Related Idioms:

**Idiom:**

"Derivative work"

**Explanation:**

Refers to a creative work that is based on or derived from another work, such as a sequel, adaptation, or remix.

## Misconceptions:

**Misconception:**

Confusing the mathematical definition of derivative with the general definition.

**Explanation:**

While the mathematical definition is a specific application of the general concept, the word derivative has broader implications beyond mathematics. It can refer to anything that is derived from another source, not just in the context of mathematical functions.