Given f x y xy x - y find all the second partial

Question

1. Given f (x, y) = xy / (x - y).

(a) Find all the second partial derivatives of this function.

(b) Find the tangent plane to the graph of this function at (2,1, 2)

2. Find the linear approximation of the function f (x, y, x) = x³√(y² +z²) at point (1, 3, 4) and use it to estimate f (.98, 3.01, 3.97).

3. If cos(xyz) = xy² + z³. Find (dz/dx) (0,2) and (dz/dy) (0,2).