>We have
    $Df(x,y,z) =\begin{bmatrix}\dfrac{\partial f}{\partial
    x}&amp;\dfrac{\partial f}{\partial y}&amp;\dfrac{\partial
    f}{\partial z}\end{bmatrix}$. The parametrization $\vec
    r(u,v)=(x,y,z)$ has derivative $D\vec r =\begin{bmatrix}
    \dfrac{\partial x}{\partial u}&amp;\dfrac{\partial x}{\partial
    v}\\ \dfrac{\partial y}{\partial u}&amp;\dfrac{\partial
    y}{\partial v}\\ \dfrac{\partial z}{\partial
    u}&amp;\dfrac{\partial z}{\partial v} \end{bmatrix}$. The
    product is $D(f(\ve