The equation given is:

$y = e^7 - x$

To find the derivative $\frac{dy}{dx}$, we need to differentiate both sides of the equation with respect to $x$.

1. The term $e^7$ is a constant, since $e^7$ is just a number, so its derivative is 0.
2. The term $-x$ has a derivative of $-1$.

Thus, the derivative is:

$\frac{dy}{dx} = 0 - 1 = -1$

So, the derivative of $y = e^7 - x$ is:

$\frac{dy}{dx} = -1$

Would you like a more detailed explanation or have any questions?

Here are some related questions for further practice:

1. What is the derivative of $y = e^k - x$, where $k$ is a constant?
2. How would you differentiate $y = e^x - x$?
3. What is the second derivative of $y = e^7 - x$?
4. How would you differentiate $y = x^2 - x$?
5. What is the derivative of $y = e^7 \sin(x)$?

Tip: When differentiating, constants like $e^7$ always have a derivative of 0!