Vocabulary

Understand the term. Connect the concept.

A practical dictionary of 512 AI, machine learning, mathematics, and programming terms from HerbDev’s AI Vocabulary app. Start with a definition, explore an example, then follow the concepts behind it.

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Derivative

Mathematics · Level 2 of 5

Derivative

The local rate at which a function's output changes with its input.

It is defined through a limit rather than a finite change alone.

Example

The slope of x squared at x equals three is six.

Listen to the definition and example

Audio transcript

Derivative. The local rate at which a function's output changes with its input. It is defined through a limit rather than a finite change alone. For example: The slope of x squared at x equals three is six.

Explore this concept

A useful analogy

A speedometer for how fast an output changes near one input value.

Why it matters

This notation connects model equations to the calculations implemented in code.

Technical detail

f′(x) = lim(h→0) [f(x+h) − f(x)] / h, when the limit exists.

Common misconception

A derivative is a local rate, not simply the function’s output divided by its input.

Start with

Function

Related concepts

Quick recall question

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