Consider the function $f : \mathbb{R}^2 \to \mathbb{R}^2$ given by $f(x,y) = (e^{2x} ,\ \sin(6xy))$.

The derivative (Jacobian matrix) of $f$ is $f'(x,y) = Df(x,y) = \begin{bmatrix}a&b\\c&d\end{bmatrix}$ where

$a =$ , $b =$ ,

$c =$ , $d =$ .