Apply Differentiation Rules (HSC SSCE Mathematics Advanced): Flashcards

$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ where $u = g(x)$

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

$\frac{dy}{dx} = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}$

For composite functions (function inside another function)

When two functions are multiplied together

When one function is divided by another

Work from outside in - differentiate outer function first

First × derivative of second + second × derivative of first

Bottom × top' - top × bottom', all over bottom squared

Identify the outermost operation in the function