The derivative of $x^8$ with respect to $x$ is:

$\frac{d}{dx}(x^8) = 8x^7$

Would you like any further clarification on this? Or do you have another question?

Here are some related questions to explore:

1. What is the derivative of $x^n$ where $n$ is a constant?
2. How do the rules of differentiation apply to products of functions, like $x^2 \cdot x^3$?
3. What happens when you differentiate more complex expressions like $\sin(x^8)$?
4. How do higher derivatives of $x^8$ change (i.e., second, third derivatives)?
5. Can you explain how to differentiate an exponential function like $e^{x^8}$?

Tip: Always use the power rule for polynomials $x^n$, where $n$ is a constant, to differentiate easily.