Show appropriate work when answering questions. (1) Differentiate the following functions. (a) y = cos2 a: (b) y = h1(a.rctan:1:) (2) Find the equation of the tangent line to the curve 3; = a: + cos a: at the point (0, 1) (3) Let 9(9) = \"39 (8.) Find 9' (a) (b) Find 9" (9) (3) Let g (a) = T\" (8.) Find 9' (6) (b) Find 9" (9) (4) Suppose the position of a particle On a string is given by 1 s=7+cos(4t) where s is measured in centimeters and t is measured in seconds. (a) Find the velocity of the particle after t seconds. Include units in your answer. (b) Find the acceleration of the particle after 15 seconds. Include units in your answer. )))