How do you find the derivative of e^(2x) using the product rule?

${e}^{2 x} = {e}^{x + x} = {e}^{x} \cdot {e}^{x}$
$f ' \left(x\right) = {e}^{x} \cdot {e}^{x} + {e}^{x} \cdot {e}^{x} = 2 {e}^{2 x}$