Last updated on Sep 20, 2026

The Quotient Rule (VCE SSCE Mathematical Methods): Quizzes

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The Quotient Rule

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What is the quotient rule formula for $F(x) = \frac{f(x)}{g(x)}$ ?

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

When is the quotient rule used?

For functions written as fractions

What condition must be satisfied to apply the quotient rule to $\frac{f(x)}{g(x)}$ ?

$g(x) \neq 0$

In the quotient rule numerator, what is the correct order of terms?

$g(x)f'(x) - f(x)g'(x)$

What is the denominator in the quotient rule result?

$[g(x)]^2$

Which rules are used together to prove the quotient rule?

Product rule and chain rule

What is $\frac{d}{d\theta}(\tan \theta)$ ?

$\sec^2 \theta$

In Leibniz notation, if $y = \frac{u}{v}$ , what is $\frac{dy}{dx}$ ?

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

For $y = \frac{\sin x}{x+1}$ , what is $\frac{du}{dx}$ where $u = \sin x$ ?

$\cos x$

For $\frac{e^x}{e^{2x}+1}$ , what is $\frac{dv}{dx}$ where $v = e^{2x}+1$ ?

$2e^{2x}$

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