The point on the plane z = 2 + x + y that is closest to the point P(0, 1, 2) is:

If φ = f(y - z, z - x, x - y), then find the value of ∂φ∂x + ∂φ∂y + ∂φ∂z.

If u = ln(x3 + y3x2 + y2), then find the value of x ∂u∂x + y ∂u∂y.

If f(x, y) = 2x2 + 2y2 + 3, what is the value of (∂f∂x + ∂f∂y)(∂f∂x - ∂f∂y) at the point (1, -2)?