Title: 11_6 Parametric Differentiation
Course: HELM Workbooks 2023-2024 > Section: HELM 11: Differentiation

Sometimes the equation of a curve is not be given in Cartesian form \(y = f(x)\) but in parametric form: \(x = h(t)\), \(y = g(t)\). In this Section we see how to calculate the derivative \( \dfrac{dy}{dx}\) from a knowledge of the so-called parametric derivatives \( \dfrac{dx}{dt}\) and\( \dfrac{dy}{dt} \). We then extend this to the determination of the second derivative \( \dfrac{d^2y}{dx^2}\).

Parametric functions arise often in particle dynamics in which the parameter \(t\) represents the time and \((x(t), y(t))\) then represents the position of a particle as it varies with time.