S R 2. Derivatives: a) Differentiate the following and do not simplify: f (x) = sin(cos(4")) [2 Marks] b) In a research laboratory, a dish of bacteria is infected with a particular disease. The equation N(d) = (15d)e 'models the number of bacteria, N, that will be infected in d days. How many days before the maximum number of bacteria will be infected? Determine the maximum number of bacteria that will be infected. Round your final answer to 2 decimal places. [4 marks]