Solve for $\epsilon(k)$ then show $\bigtriangledown \epsilon$ is normal to $\epsilon_n(k)$

Question

Given that

$$g(\epsilon) = 2 \int \frac{d^3k}{(2\pi^3)} \delta[\epsilon - \epsilon_n(k)]$$

Find $\bigtriangledown \epsilon_n(k)$ and show it is a vector normal to $\epsilon = \epsilon_n(k)$.

Don't know how to evaluate the integral with the $\delta$ in it, and even if I could, how could I show it's normal to this particular type of surface?