October 2021 Paper 2 Q1
1 Differentiate the following with respect to \(x\).
(a) \(\mathrm{e}^{-4x}\) [2]
(b) \(\dfrac{x^2}{x + 1}\) [2]
| Scheme | Marks |
|---|---|
| \(-4\mathrm{e}^{-4x}\) oe | B2 |
| [2] |
Notes
B2: B1 for \(\mathrm{e}^{-4x}\) seen as part of answer, not in denominator
| Scheme | Marks |
|---|---|
| By quotient rule \(\dfrac{(x + 1) \times 2x - x^2 \times 1}{(x + 1)^2}\) | B1 B1 |
| \(\left(= \dfrac{x(x + 2)}{(x + 1)^2} \text{ or } \dfrac{x^2 + 2x}{x^2 + 2x + 1}\right)\) | |
| [2] |
Notes
B1: correct denominator & 1 correct term in numerator, any form
B1: ISW
Alternative method
| Scheme | Marks |
|---|---|
| chain rule or \(-(x + 1)^{-2} \times x^2 + (x + 1)^{-1} \times 2x\) | B1 B1 |
B1 for either term correct
B1: ISW