#### Answer

$e^{5x}$

#### Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$
After simplifying, the determinant of this matrix will be:
$det =(e^{2x})(3e^{3x})-(2e^{2x})(e^{3x})$
or, $=3e^{5x}-2e^{5x}$
or, $=e^{5x}$