What is the Jacobian matrix of the following. $$
\frac{dx}{dt} = \left(1−x−\frac y2\right)x
\\
\frac{dy}{dt} = \left(1- \frac x3−y\right)y
$$
I am unsure about his to take the partial derivatives of these differential equations
$$
\begin{array}{cc}
  \frac{\partial}{\partial x} (dx/dt) = 1-2x-y/2, &amp; 
  \frac{\partial}{\partial x} (dy/dt) = -y/3 \\
  \frac{\partial}{\partial y} (dx/dt) = -x/2, &amp;
  \frac{\partial}{\partial y} (dy/dt) = 1 - x/3 -2y. \\
\end{array}
$$
$$
\begin{array}{cc}
  \frac{\partial}{\partial x} (dx/dt) = 1-2x-y/2, &amp; 
  \frac{\partial}{\partial x} (dy/dt) = -y/3 \\
  \frac{\partial}{\partial y} (dx/dt) = -x/2, &amp;
  \frac{\partial}{\partial y} (dy/dt) = 1 - x/3 -2y. \\
\end{array}
$$