Parametric Differentiation (AQA A-Level Mathematics): Flashcards

$\frac{dy}{dx}$

Finding derivatives where $x$ and $y$ are functions of parameter $t$

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

$\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}$

Slope, concavity, and other curve properties

$-\frac{1}{m}$ where $m$ is gradient of tangent

$y - y_1 = m(x - x_1)$

Differentiate $x=f(t)$ and $y=g(t)$ w.r.t. $t$

Eliminate parameter $t$ from equations

$\frac{1}{\frac{dx}{dt}}$ (reciprocal)