Please answer the following questions below, Please make sure that your writing is clear, neat, concise and easy to read/follow thankyou

When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: 0 Provide full solutions. showing all of your steps. 0 Make sure that there is one step or idea per line. 0 Use one equal sign per line. 0 Make sure that equal signs line up vertically. 0 Don't use self-developed short form notations. 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=]n(4:i:2+4} b.y=% c. y = 25s+7(h1[5a: + 1)} _ M3 ill-m 2. Use the process of implicit differentiation to nd % given that 9.73:3gr ye\" = l}. [4 marks} i 3. Use curve sketching methods, sketch the graph of the function given by the equation 1,- = E: . Make sure that you include all steps, charts, and derivations details. {10 marks} 3 _ I. 4. Use logarithmic differentiation to nd the derivative of the function y = W. [6 marks} 5. The population, P, of an island, 3; 1years after colonization is given by the function P = 250 1+4e= ' 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. lGive a possible explanation for the shape of the curve. [3 marks}