As part of a question set, there is a question to find the gradient vector / Jacobian Matrix of a function $f(x,y)=cos(2x)sin(y)$. All of the examples that I have seen for finding the Jacobian matrix (and all information in the lecture notes) has the function resulting in a square matrix; however, I do not believe that this would be the case for this function.
I have found the gradient vector, $\nabla f$ as $\nabla f = \begin{pmatrix}\frac{\partial f}{\partial x} \\\frac{\partial f}{\partial y}\end{pmatrix} = \begin{pmatrix}-2\sin{2x}\sin{y}\\\cos{2x}\cos{y}\end{pmatrix}$.
Is the Jacobian Matrix, $D_{f}$ in the form $D_{f}=\begin{pmatrix}\frac{\partial f}{\partial x} & \frac{\partial f}{\partial y}\end{pmatrix} = \begin{pmatrix}-2\sin{2x}\sin{y} & \cos{2x}\cos{y}\end{pmatrix}$?