The Quotient Rule (VCE SSCE Mathematical Methods): Flashcards

Differentiating functions written as fraction of two functions

$F'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{[g(x)]^2}$

Denom × deriv of num - num × deriv of denom, over denom squared

$g(x) \neq 0$

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

$\sec^2 \theta$

Using the product rule and chain rule together

Order in numerator crucial: $g \cdot f' - f \cdot g'$ (not reversed)

The square of the denominator: $[g(x)]^2$

Cannot do this; must use quotient rule