# What is the derivative of (e^(2x)sin(3x))?

I would use the Product Rule between functions $e$ and $\sin$ and the Chain Rule to deal with the exponent and argument:
$f ' \left(x\right) = 2 {e}^{2 x} \sin \left(3 x\right) + {e}^{2 x} 3 \cos \left(3 x\right) =$
$= {e}^{2 x} \left[2 \sin \left(3 x\right) + 3 \cos \left(3 x\right)\right]$