c r(u,v))) =\begin{bmatrix} \dfrac{\partial
    f}{\partial x}\dfrac{\partial x}{\partial u}+ \dfrac{\partial
    f}{\partial y}\dfrac{\partial y}{\partial u}+ \dfrac{\partial
    f}{\partial z}\dfrac{\partial z}{\partial u}&amp;
    \dfrac{\partial f}{\partial x}\dfrac{\partial x}{\partial v}+
    \dfrac{\partial f}{\partial y}\dfrac{\partial y}{\partial v}+
    \dfrac{\partial f}{\partial z}\dfrac{\partial z}{\partial v}
    \end{bmatrix} $. The first column is $\dfrac{\partial
    f}{\partial u}$, and th