Parametric Equations

If a particle is moving in the plane, its position (x, y) at time t will be given by a pair of equations

x = f(t), y = g(t).

These are called parametric equations. The slope of the curve traced out by this particle can be found by the Chain Rule,

,

whenever the derivatives exist and f'(t) ≠ 0. This is a Chain Rule application of type (2).