Given g(x) = 4* sin (3*x), find the value of g'(pi/3).

Using the table of standard derivatives given at the beginning of the Higher Paper we have, for f(x) = sin(ax), f'(x) = a * cos (ax)and so with this we have, g(x) = 4 * sin(3x), g'(x) = 4 * 3 * cos(3x) = 12 * cos(3x).Evaluating g'(x) at x = pi/3 we have, g'(pi/3) = 12 * cos (3(pi/3)) = 12 * cos(pi) = 12 * (-1) = -12.