Please explain all steps in detail from your own work for good feedback.

8. To differentiate each inverse trigonometric lnction shown, begin by expressing x in terms of 31. Then differentiate both sides with respect to A: and solve for dyfdx. You will need to use a trigonometric identity to express dyg'dx in terms of x. a] b] C] 11] Differentiate y = sin'1 3: with respect to x. Differentiate y = cos'1 x with respect to x. Differentiate \"y = tan1 :5 with respect to x. Differentiate y = sec'1 :5 with respect to x. 9. To gain a clearer understanding ofthe derivative of 2", lets take a visual approach. a] b] C] d] 9] Draw the graph offIEx) = 2\". Draw points ( 3, :3] . (13), (1.3, (Ill. 1]. (1, 2), (2. 4], (3, 3]. For each pair of adjacent points. write down the slope of the line segment that connects thenL Explain what the Mean Value Theorem reveals about this function. Use this to sketch the graph of f'{x) on the same coordinate plane as your graph of f [3:] Compare the two graphs. Explain in words how they are similar and how they are different 10. Repeat all the steps of exercise 9 for the function 31li = 45'". Use the following points: (2. 3- (1.3: (2, a), m (5-2} cm- (3,3)