compute each of the problem completely. (Partial Derivatives) 1) compute ∂z/∂s and ∂z/∂t for z=x²y, x = sin (2πst ³), y = qs²t
2) z³ - 3x ²y + 6 xyz = 0; use the method of partial differentiation to find
∂z/∂y, ∂z/∂y
3) Suppose z = xe^2x cos 3y, find all the first and all the second derivatives. 4) Angle A of triangle ABC is decreasing at the rate of 4. degrees per second, while sides AB and Ac are increasing at the rates of 4 and 5 meters per second respectively. If at certain instant A-45 degrees, AB 10m, Ac 7m, how fast is the area of the triangle changing? 5) water is leaking out of a conical tank at the rate of 0.5m³/min The tank is also stretching in such a way that, while it remains conical, the distance across the top at the water surface is increasing at the rate of 0.2 m/min. How fast is the height of water changing at the instant when h 10 and the volume of water is 75m³ ?