Quick questions on Differentiation from the standard rules explained: O-Level A-Maths

5short 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 rewriting before differentiating?

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Roots and reciprocals must be rewritten as powers first:

\sqrt{x} = x^{1/2}

and

\dfrac{1}{x} = x^{-1}

. Then the power rule applies directly, and you tidy negative or fractional indices back at the end.

What is sign of the cosine derivative?

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\dfrac{d}{dx}\cos x = -\sin x

; forgetting the minus is a frequent error.

What is q1?

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Differentiate

y = x^5

. [1 mark]

What is q2?

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Differentiate

y = 4\sqrt{x}

. [2 marks]

What is q3?

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Find

\dfrac{dy}{dx}

for

y = e^x - 3\cos x

. [2 marks]

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