# What is the relation between limits, derivatives and instantaneous rate of change?

##### 1 Answer

Oct 16, 2015

Both derivatives and instantaneous rates of change are defined as limits.

#### Explanation:

Depending on how we are interpreting the difference quotient we get either a derivative, the slope of a tangent line or an instantaneous rate of change.

A derivative is defined to be a limit. It is the limit as

The instantaneous rate of change is also a limit. It is a limit of an average rate of change. Because the average rate of change is expressed as