# Definition:Rate of Change

## Definition

The **rate of change** of a physical quantity is its (first) derivative with respect to an independent variable which is usually, but not exclusively, time.

Loosely speaking, it means **how fast something changes**, with a wider scope than change in physical displacement.

### Time

When the independent variable of a **rate of change** is time, it is commonplace to take that fact for granted, and refer merely to its **rate of change**.

### Rate of Increase

A **rate of increase** is a **rate of change** measured in a strictly positive direction.

### Rate of Decrease

A **rate of decrease** is a **rate of change** measured in a strictly negative direction.

Hence a negative **rate of decrease** is a **rate of increase**.

### Dimension

Let a physical quantity $P$ have dimension $\mathsf D$.

Then the **rate of change** of $P$ with respect to time has dimension $\mathsf {D T}^{-1}$.

## Also see

- Results about
**rate of change**can be found here.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**rate of change**