Quick questions on Differentiation rules: N(A)-Level Additional Mathematics

8short 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 the power rule?

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For a power of

x

, multiply by the power and reduce the power by one:

What is the product rule?

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For a product

y = uv

of two functions:

What is the quotient rule?

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For a quotient

y = \dfrac{u}{v}

What is quotient-rule order?

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The numerator is

v\,u' - u\,v'

, not the other way round; the wrong order flips the sign.

What is not rewriting roots first?

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\dfrac{1}{x^2}

should be written

x^{-2}

before differentiating to

-2x^{-3}

What is q1?

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Differentiate

y = 5x^3

. [1 mark]

What is q2?

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Differentiate

y = (4x - 3)^2

using the chain rule. [2 marks]

What is q3?

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Differentiate

y = \dfrac{1}{x}

by writing it as a power. [2 marks]