Just a graphical representation of what @Mr Tsjolder has said:
The Input for the network is $\mathbf{X}$
and
Let's take the network $\mathbf{O}$=$\mathbf{W}$*$\mathbf{X}$ (We can any other relationship also!! This is just an example!!)
The Jacobian of this network would then simply be $\mathbf{J} = \frac{\partial {\mathbf{O}}}{\partial{\mathbf{X}}}$