El Jacobiano es
J(r,v)=∂(x,y)∂(x,v)=∣∂y∂u∂y∂v∂y∂r∂y∂θ∣=∣2uv−2vu∣=2u2+2v2J(r,v) = \frac{\partial(x,y)}{\partial(x,v)} = \begin{vmatrix} \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}\\ \\ \frac{\partial y}{\partial r} & \frac{\partial y}{\partial \theta} \end{vmatrix} = \begin{vmatrix} 2u & v\\ -2v & u \end{vmatrix} = 2u^2 + 2v^2J(r,v)=∂(x,v)∂(x,y)=∣∣∂u∂y∂r∂y∂v∂y∂θ∂y∣∣=∣∣2u−2vvu∣∣=2u2+2v2