Differentiate 4x³ln(2x + 1) with respect to x.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

1. [M1] (a) for differentiation of a correct product
2. [A2, 1, 0] -1 for each error
3. [M1] (b) (i) for differentiation of a quotient involving (x + 2)^(1/2)
4. [A1] all correct unsimplified
5. [DM1] for attempt to simplify
6. [A1] for correct simplification to obtain the given answer
7. Or:
8. [M1] for differentiation of a product involving (x+2)^(-1/2)
9. [A1] all correct unsimplified
10. [DM1] for attempt to simplify
11. [A1] for correct simplification to obtain the given answer
12. [M1] (b) (ii) for 10x / (√x+2) or 5 * 2x / (√x+2)
13. [A1] correct only, allow unsimplified. Condone omission of + c
14. [M1] (b) (iii) for correct application of limits in their answer to (b)(ii)
15. [A1] for 40/3