Quotient Rule (AQA A-Level Mathematics): Flashcards

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Quotient Rule
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Purpose of quotient rule?

Used to differentiate quotient of two functions

Quotient rule: ddx(uv)=\frac{d}{dx}(\frac{u}{v})=

vu′−uv′v2\frac{vu'-uv'}{v^2}

In quotient rule, u(x)u(x) is?

Numerator

In quotient rule, v(x)v(x) is?

Denominator

In quotient rule, u′(x)u'(x) is?

Derivative of numerator

Denominator in quotient rule result?

[v(x)]2[v(x)]^2 (square of denominator)

ddx(x2+1x2−1)=\frac{d}{dx}(\frac{x^2+1}{x^2-1})=

−4x(x2−1)2\frac{-4x}{(x^2-1)^2}

ddx(sin⁡(x)x)=\frac{d}{dx}(\frac{\sin(x)}{x})=

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

When to combine quotient rule with chain rule?

When functions involved are composite

First step applying quotient rule?

Identify u(x)u(x) (numerator) and v(x)v(x) (denominator)

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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