CAIE IGCSE Additional Math 14.3 Differentiate Standard Functions Questions

Practise differentiating rational powers, trigonometric functions and composite expressions with constant multiples, sums and the chain rule in Cambridge Additional Mathematics.

Exam points

Differentiate standard powers, trigonometric functions and composite functions, using constant multiples and the chain rule.

[Maximum number: 3]

Given that $y=\frac{4 x^{3}-5}{x^{2}}$ , show that $\frac{\mathrm{d} y}{\mathrm{~d} x}$ can be written as $\frac{2\left(2 x^{3}+5\right)}{x^{3}}$ .

Attempts to find $y=4 x-5 x^{-2}$
at least one term correct

$\frac{\mathrm{d} y}{\mathrm{~d} x}=4+10 x^{-3}$
Correct completion to given answer $\frac{2\left(2 x^{3}+5\right)}{x^{3}}$
Alternative version

$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{12 x^{4}-8 x^{4}+10 x}{x^{4}}$ or equivalent
unsimplified form

M1 for an attempt at the quotient rule with correct structure
$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x^{2}\left(\text { their } 12 x^{2}\right)-\left(4 x^{3}-5\right)(\text { their } 2 x)}{\left(x^{2}\right)^{2}}$

Correct completion to given answer $\frac{2\left(2 x^{3}+5\right)}{x^{3}}$

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CAIE IGCSE Additional Math 14.3 Differentiate Standard Functions Questions question 1