Find the jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. if x = f(u, v, w), y = g(u, v, w), and z = h(u, v, w), then the jacobian of x, y, and z with respect to u, v, and w is ∂(x, y, z) ∂(u, v, w) = ∂x ∂u ∂x ∂v ∂x ∂w ∂y ∂u ∂y ∂v ∂y ∂w ∂z ∂u ∂z ∂v ∂z ∂w . spherical coordinates x = ρ sin φ cos θ, y = ρ sin φ sin θ, z = ρ cos φ