Definition:Derived Curve

Definition

Let $y = \map f x$ be the locus of a curve embedded in the Cartesian plane.

The derived curve of $y = \map f x$ is the curve:

$y = \map {f'} x$

where $f'$ denotes the (first) derivative of $f$.

Examples

Velocity Curve

Let $y = \map f x$ be the locus of a curve representing distance with respect to time.

The derived curve $y = \map {f'} x$ then represents velocity with respect to time.

Acceleration Curve

Let $y = \map f x$ be the locus of a curve representing velocity with respect to time.

The derived curve $y = \map {f'} x$ then represents acceleration with respect to time.

Also see

• Results about derived curves can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): derived curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): derived curve