Quotient Rule (Edexcel A-Level Mathematics): Quizzes

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

vu′−uv′v2\frac{vu' - uv'}{v^2}

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

The denominator

What is the denominator of the quotient rule result?

[v(x)]2[v(x)]^2

What is the first step in applying the quotient rule?

Identify 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}

For y=exln⁡(x)y = \frac{e^x}{\ln(x)}, what is u′(x)u'(x)?

exe^x

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

3e3x3e^{3x}

What is dydx\frac{dy}{dx} for y=4x+c4x−cy = \frac{4x + c}{4x - c} (where c≠0c \neq 0)?

−8c(4x−c)2\frac{-8c}{(4x-c)^2}

Why does y=4x+c4x−cy = \frac{4x + c}{4x - c} have no stationary points when c≠0c \neq 0?

dydx=−8c(4x−c)2\frac{dy}{dx} = \frac{-8c}{(4x-c)^2} never equals 0

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Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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