Product Rule (HSC SSCE Mathematics Advanced): Flashcards

Differentiate product of two functions

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

First × deriv. of second + second × deriv. of first

NOT $\frac{du}{dx} \cdot \frac{dv}{dx}$

First function

Second function

When expansion complicated or has composite functions

Simple products creating straightforward polynomials

Chain rule

Makes derivative cleaner and easier to work with