Parametric Differentiation (Edexcel A-Level Mathematics): Flashcards

To define $x$ and $y$ as functions of a parameter $t$.

$dy/dx = (dy/dt) / (dx/dt)$ using the chain rule.

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

Differentiate $x = f(t)$ and $y = g(t)$ with respect to $t$.

Use $y - y_1 = m(x - x_1)$ with $m = \frac{dy/dt}{dx/dt}$.

Differentiate $x$ and $y$, then divide $dy$ by $dx$.

The point is $(\sqrt{2}, \sqrt{2})$ when $\theta = \pi/4$ on the curve.

Solve $t - 1 = 3(1/(t+1))$.

$y = 2(x + 1) - 1$, normal point $(-1, -1)$.

The Cartesian equation is $y = \frac{1}{x} - 2$.