The derivative of $e^y$ with respect to $y$ is:

$\frac{d}{dy} e^y = e^y$

The function $e^y$ differentiates to itself, as the exponential function is unique in having this property.

Would you like further details or have any specific questions?

Here are a few related questions that expand on this concept:

1. What is the derivative of $e^{2y}$ with respect to $y$?
2. How does the chain rule apply to derivatives involving $e^y$?
3. What is the second derivative of $e^y$ with respect to $y$?
4. How does $e^y$ behave as $y \to \infty$?
5. What are the applications of $e^y$ in real-world scenarios?

Tip: The exponential function $e^x$ is one of the few functions that equals its own derivative, making it especially useful in differential equations.