Answer
$1+8uvw$
Work Step by Step
$Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial u}&\dfrac{\partial x}{\partial v}&\dfrac{\partial x}{\partial w}\\\dfrac{\partial y}{\partial u}&\dfrac{\partial y}{\partial v}&\dfrac{\partial y}{\partial w}\\\dfrac{\partial z}{\partial u}&\dfrac{\partial z}{\partial v}&\dfrac{\partial z}{\partial w}\end{vmatrix}$
Now, $Jacobian=\begin{vmatrix} 0&1&2w\\2u&0&1\\1&2v&0\end{vmatrix}=0-1(0-1)+2w(2u \cdot 2v -0)=1+8uvw$
