# derivative

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### Pronunciation

• (UK) IPA: /dɪˈrɪvətɪv/
•  Audio (US) (file)

 Positive derivative Comparative none Superlative none
1. If something is derivative, it is obtained from something else

## Noun

A function (black) and a tangent (red). The derivative at the point is the slope of the tangent.
1. (countable) A derivative is something which is based on another.
2. (calculus) A derivative is the derived function]] of another function (the slope at a certain point on some curve ${\displaystyle f(x)}$)
The derivative of ${\displaystyle f:f(x)=x^{2}}$ is ${\displaystyle f':f'(x)=2x}$
3. (calculus) The value of this function for a given value of its independent variable.
The derivative of ${\displaystyle f(x)=x^{2}}$ at x = 3 is ${\displaystyle f'(3)=2*3=6}$.