The image shows a limit problem: $\underset{x\to 0}{\lim }\frac{e^{2x}-1}{x}$. This is a standard indeterminate form (0/0). The derivative of $e^u$ is $e^u·\frac{du}{dx}$. Here, the limit is the derivative of $e^{2x}$ at x=0, which is $2e^{2·0}=2$.

Final answer: $2$