Say I have a function $f(p) : \mathbb{R}^3 \to \mathbb{R}$, where $p = (x,y,z)^T$. I know that the Jacobian $J$ is $f_p = (f_x, f_y, f_z)$. I know that the time derivative of the Jacobian, $J'$, is $\dfrac{\partial J}{\partial p} \cdot\dfrac{dp}{dt}$. The quantity $\dfrac{dp}{dt}$ is simply the velocity $v$ at $p$. But what is $\dfrac{\partial J}{\partial p}$? Is it the Jacobian of the Jacobian? How can I express this as a matrix (and not a tensor)?
Context: I am trying to apply equation (11) of Constrained Dynamics.
