Find \(g'(x)\) .

Find the gradient of the graph of g at \(x = \pi \) .

evidence of choosing the product rule     (M1)

e.g. \(uv' + vu'\)

correct derivatives \(\cos x\) , 2     (A1)(A1)

\(g'(x) = 2x\cos x + 2\sin x\)     A1     N4

[4 marks]

attempt to substitute into gradient function     (M1)

e.g. \(g'(\pi )\)

correct substitution     (A1)

e.g. \(2\pi \cos \pi  + 2\sin \pi \)

\({\text{gradient}} = - 2\pi \)     A1     N2

[3 marks]

Most candidates answered part (a) correctly, using the product rule to find the derivative, and earned full marks here. There were some who did not know to use the product rule, and of course did not find the correct derivative.

In part (b), many candidates substituted correctly into their derivatives, but then used incorrect values for \(\sin x\) and \(\cos x\) , leading to the wrong gradient in their final answers.