Hi, I had trouble understanding these questions. Could you please show the work so I can understand the concepts that are being applied? Thanks so much :)

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?(1 point) You are standing above the point [5, 1} on the surface 3 = 25 (m2 l 9'2). [a] In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction = C] [b] If you start to move in this direction, what is the slope of your path? slope = C] Find the equation of the tangent plane to the surface 3:2 4y2 222 | myz = 42 at the point (:11, y, z) = (4, 2, 3) Z