I am having some trouble with these problems, thank you for your help

If z = x'y + 3xy where x = sin 2t and y = cost find dz /dt when t = 0.Let F = (332,332) and C be any curve from (0,1) to (1,3). . Show that F is conservative. Evaluate j F'dr where F = (yi e, 2:1: +003 132) and C' is the positively oriented boundary P of the region enclosed by the parabolas y = 3:2 and :1: = y2