MAT 271 Problem Set #3: Advanced Derivatives Spring 2018 Instructions: Work the following exercises out by hand on separate paper. Clearly label each exercise and indicate your nal answer. You must show all work for full credit. I. Calculate each derivative: 1) i [59:2 sin x] 2) % [csc 3t] 3) i [sz'l] 4) i W + 8x 3] dx 3x+2 5) imq'tt6 3t)] 6) jx[cos3x] d t2 3: d 7) E[2t:7] 8) a[3x*secx*d2x+5] ll. Suppose the position of an object moving horizontally after tseconds is given by the function s(t), where sis measured in feet, with s > 0 corresponding to positions right of the origin. For each of the given position functions and time intervals, answer the following questions. a) Find the velocity function. b) When is the object stationary? Moving to the right? Moving to the left? c) Determine the velocity and acceleration of the object at t = 2. d) Determine the acceleration of the object when the velocity is zero. 9) s(t)=6t3t2,05t53 10) s(t)=t36t, 05:54