June 2024 Paper 2 Q5
5 Given that
\[y = \frac{x^3}{\sin x}\]find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) [3 marks]
| Scheme | Marks | AO |
|---|---|---|
| Differentiates \(x^3\) and \(\sin x\) to obtain \(3x^2\) and \(\cos x\) OE | B1 | 1.1b |
| Uses the quotient rule and obtains numerator \(Ax^2\sin x \pm Bx^3\cos x\) Condone any denominator Or Writes as a product and applies the product rule to obtain \(Ax^2\operatorname{cosec}(x) \pm x^3\operatorname{cosec}(x)\cot(x)\) | M1 | 3.1a |
| Obtains \(\dfrac{3x^2\sin x - x^3\cos x}{\sin^2 x}\) ACF No ISW | A1 | 1.1b |
| (3 marks) |