Differential Quotient

analysis

Definition

Differential Quotient

The differential quotient (or derivative) of a function at a point is the limit of the difference quotient as the interval approaches zero.

The difference quotient represents the slope of the secant line through and :

The differential quotient is the slope of the tangent line at :

Significance

The differential quotient provides a formal way to calculate the instantaneous rate of change of a function. If this limit exists at , the function is said to be differentiable at that point.