Quotient Rule (AQA A-Level Mathematics): Quizzes

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Quotient Rule
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What is the quotient rule for ddx(uv)\frac{d}{dx}\left(\frac{u}{v}\right)?

vu′−uv′v2\frac{vu' - uv'}{v^2}

In the quotient rule formula, what does u(x)u(x) represent?

The numerator

Why is the denominator squared in the quotient rule formula?

To account for how the denominator changes

What is the first step when applying the quotient rule?

Identify functions u(x)u(x) and v(x)v(x)

What is dydx\frac{dy}{dx} for y=x2+1x2−1y = \frac{x^2 + 1}{x^2 - 1}?

−4x(x2−1)2\frac{-4x}{(x^2 - 1)^2}

What is dydx\frac{dy}{dx} for y=sin⁡(x)xy = \frac{\sin(x)}{x}?

xcos⁡(x)−sin⁡(x)x2\frac{x\cos(x) - \sin(x)}{x^2}

When must the quotient rule be combined with the chain rule?

When the functions are composite functions

For y=x2e3xy = \frac{x^2}{e^{3x}}, what is v′(x)v'(x) where v(x)=e3xv(x) = e^{3x}?

3e3x3e^{3x}

For y=4x+c4x−cy = \frac{4x + c}{4x - c} with c≠0c \neq 0, why are there no stationary points?

dydx=−8c(4x−c)2≠0\frac{dy}{dx} = \frac{-8c}{(4x-c)^2} \neq 0

What is the simplified form of dydx\frac{dy}{dx} for y=x2e3xy = \frac{x^2}{e^{3x}}?

2x−3x2e3x\frac{2x - 3x^2}{e^{3x}}

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