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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!

Find the derivative of the equation y = e^7 - x.

This problem explains how to find the derivative of y = e^7 - x. It covers key calculus concepts, such as the differentiation of constant and linear functions, and is suitable for students in Grades 11-12.

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