| Date | November 2009 | Marks available | 2 | Reference code | 09N.2.sl.TZ0.2 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(f(x) = \cos 2x\) and \(g(x) = \ln (3x - 5)\) .
Find \(f'(x)\) .
Find \(g'(x)\) .
Let \(h(x) = f(x) \times g(x)\) . Find \(h'(x)\) .
Markscheme
(a) \(f'(x) = - \sin 2x \times 2( = - 2\sin 2x)\) A1A1 N2
Note: Award A1 for 2, A1 for \( - \sin 2x\) .
[2 marks]
\(g'(x) = 3 \times \frac{1}{{3x - 5}}\) \(\left( { = \frac{3}{{3x - 5}}} \right)\) A1A1 N2
Note: Award A1 for 3, A1 for \(\frac{1}{{3x - 5}}\) .
[2 marks]
evidence of using product rule (M1)
\(h'(x) = (\cos 2x)\left( {\frac{3}{{3x - 5}}} \right) + \ln (3x - 5)( - 2\sin 2x)\) A1 N2
[2 marks]
Examiners report
Almost all candidates earned at least some of the marks on this question. Some weaker students showed partial knowledge of the chain rule, forgetting to account for the coefficient of \(x\) in their derivatives. A few did not know how to use the product rule, even though it is in the information booklet.
Almost all candidates earned at least some of the marks on this question. Some weaker students showed partial knowledge of the chain rule, forgetting to account for the coefficient of \(x\) in their derivatives. A few did not know how to use the product rule, even though it is in the information booklet.
Almost all candidates earned at least some of the marks on this question. Some weaker students showed partial knowledge of the chain rule, forgetting to account for the coefficient of x in their derivatives. A few did not know how to use the product rule, even though it is in the information booklet.
