Implicit Differentiation (AQA A-Level Mathematics): Flashcards

Finding derivative when $y$ not explicitly solved for in terms of $x$

Implicit equations, relations, circles (where $y$ not isolated)

$\frac{d}{dy} \times \frac{dy}{dx}$

$2y \frac{dy}{dx}$

1. Diff both sides w.r.t. $x$, 2. Collect $\frac{dy}{dx}$ terms, 3. Solve for $\frac{dy}{dx}$

Chain rule (introduces $\frac{dy}{dx}$)

$\frac{-x}{y}$

Tangent/normal lines, related rates, inverse function derivatives

$y + x\frac{dy}{dx}$

Set $\frac{dy}{dx} = 0$ and solve