I need help understanding these 3 question if you can please show the work, I didn't know how to solve. Thank you

If z = sin(3x ) cos(y), with x = 4et and y = 5 + t , then dz dt (x,y)=(4e3,14) isFor the function an, y) = 3m2'75y3, find the directional derivative at (2, 5) in the direction 9 = 41r/3 : D A happy heat-loving bug is wandering on a hot plate. The temperature at any point on the plate is given by T(x, y) = 190e (22/3)-(y2/5) If the bug is at the point P = (-3, 1) and moving towards the point Q = (2, -1), what is the rate of change in the temperature in the direction of its motion? In what direction should the bug move from P for the temperature to increase the fastest? (Give your answer as a unit vector.) What is the magnitude of the rate of change of temperature in that direction