The Chain Rule (VCE SSCE Mathematical Methods): Flashcards

Composite function

Inside function

Outside function

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

$q'(x) = f'(g(x)) \cdot g'(x)$

Derivative of outside × derivative of inside

$g$ differentiable at $x$ and $f$ differentiable at $g(x)$

Identify inside and outside functions

Efficient differentiation without expanding composite functions

$u = x^3 + 1$