Implicit Differentiation (Leaving Cert Mathematics): Flashcards

A technique to find the derivative when $y$ is not explicitly solved for $x$

When $y$ is not isolated on one side of equation

Differentiate both sides with respect to $x$, treating $y$ as a function of $x$

Treat $y$ as a function of $x$

Chain rule: rac{d}{dx} y = rac{dy}{dx}

Collect terms with rac{dy}{dx} on one side

Solve for rac{dy}{dx}

rac{dy}{dx} = rac{-x}{y}

2x + 2y rac{dy}{dx} = 0

rac{dy}{dx} = rac{6y - 3x^2}{3y^2 - 6x}

6(x rac{dy}{dx} + y) using product rule

A circle