Note that derivatives must be fully simplied for full marks on this assignment. 1. Find the derivatives of each of these functions: (2 marks each) a. y = 111(4m2 + 4) 2a:4 951 C. y = 25z+7(1n(51 + 1)) 413 EM+CEA d.y= 2. Use the process of implicit differentiation to find 2% given that waey 7 yem = 0. (4 marks) 3. Use curve sketching methods, sketch the graph of the function given by the equation y = 5. Make sure that you include all steps, charts, and derivations details. (10 marks) _ (22+5)3(52221)4 4. Use logarithmic differentiation to find the derivative of the function y _ m .(6 marks) 250 1+4e'01'1y - 5. The population, P, of an island, y years after colonization is given by the function P = a. What was the initial population of the island? (2 marks) b. How long did it take before the island had a population of 150'? (2 marks) c. After how many years was the population growing the fastest? (3 marks) d. Using curve sketching methods, sketch the graph of the function. Make sure that you include all steps, charts, and derivations details. (10 marks) e. Give a possible explanation for the shape of the curve. (3 marks) Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will contribute to your overall final grade in this course