Chain Rule (HSC SSCE Mathematics Advanced): Flashcards

Differentiate composite functions

One function's output used as another function's input

Function evaluated first

Function applied to result of inner function

$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$

$n[f(x)]^{n-1} \times f'(x)$

Operation performed last

Differentiate outside × derivative of inside

Convert to index form first

Substitute back to express in terms of original variable