Derivative of a parametric function

Definition

The derivative of a parametric function represents the rate at which the y-coordinate changes with respect to the x-coordinate. It measures how fast the curve is changing at any given point.

Analogy

Think of driving on a curvy road where your position is described by x and y coordinates. The derivative of a parametric function is like your speedometer, telling you how fast your y-coordinate (position) is changing as you move along the x-axis (road).

Related terms

dy/dx: This notation represents the derivative of y with respect to x in terms of parametric equations.

Second Derivative of Parametric Equations: This refers to taking the derivative twice, representing how quickly the rate of change is changing for a parametric function.

Tangent Line: A line that touches a curve at one point and has the same slope as that point's derivative.