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. 1. Find the derivatives of each of these functions. {4 marks each} a. y = [z'+csc(z}]3 sec-b; sinm lay: c. y = cat-(m) 2. Use the process of implicit differentiation to nd % given that sin (4:12} + sin {2y} = 1 . ldmarksil 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch the graph ofthe given function on the interval 2:Ir g m :3. 271'. [4 marks} _ nos (29:)- y _ 3 23in\" (x) 4. Find the equation of the tangent to the curve 1,.- = \"in 3\"\" at it: = {-16 marks] GIL'IS :13 5. The movement of the crest of a wave is modelled with the function h {t} = . 2 cos [4f] + O. 3 sin [5t}. Find the maximum height ofthe wave and the time at which it occurs. [6 marks} 6. Determine the 19th derivative of the function y = sin {2:}. Fully explain the process you used to determine this. (4 marks}