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A2 1 Pure Mathematics

Quick questions on Differentiation: the chain, product and quotient rules, implicit differentiation and rates of change - CCEA A-Level Mathematics

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is connected rates of change?
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When two quantities both change with time, the chain rule connects their rates: dVdt=dVdrdrdt\dfrac{dV}{dt} = \dfrac{dV}{dr}\dfrac{dr}{dt}. This lets you find one rate from another, for example the rate a radius grows from the rate a volume is added.
What is q1?
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Differentiate y=e5xy = e^{5x}. [1 mark]
What is q2?
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Differentiate y=x2ln⁡xy = x^2\ln x. [2 marks]
What is q3?
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Differentiate ddxy3\frac{d}{dx}y^3 implicitly. [1 mark]

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