please do the following problems and show the work

33. Let. y = aretan 1'. {a} Solve for 1'. {h} Take the derivative of both sides of your equation from part [a]. Emp1oy the ehain rule every time you need to apply the i to a Ell-variable. is {e} Solve for . Use your equation from part [a] to 1pyrite your answer as a function is of I. {:21} Use your result to complete the following Theorem. Theorem 4U [Derivative of the Inverse Tangent} r! arctans' = is 84. (a) Sketch an accurate graph of the cosine on the domain (-2x, 2x). Use this to sketch an accurate graph of the secant function on the same set of axes. (b) Identify at least three domains of length * where the secant is one-to-one. 85. (a) Sketch y = secr on a restricted domain of length ~ where the function is one-to- one. Choose such a domain with angles in Quadrants 1 and 3 only. (b) Sketch a graph of the inverse secant function defined using this domain restriction. (c) Give the domain and range of the inverse secant according to this definition. (d) Give the open intervals where the inverse secant is increasing or decreasing. What does this tell you about the derivative of the inverse secant? (e) Show that dy 1 dr TV