The given function is $f(x) = x^7$.

To find the derivative of this function, we apply the power rule. The power rule states that for a function $f(x) = x^n$, its derivative is given by:

$f'(x) = n \cdot x^{n-1}$

For $f(x) = x^7$, we can apply this rule:

$f'(x) = 7 \cdot x^{7-1} = 7x^6$

Thus, the derivative of $f(x) = x^7$ is:

$f'(x) = 7x^6$

Would you like further details on this process or have any questions?

Here are some related questions:

1. What is the derivative of $f(x) = x^5$?
2. How do you apply the power rule to a function like $f(x) = x^{10}$?
3. What happens if the exponent is a fraction, like in $f(x) = x^{1/2}$?
4. How would you differentiate $f(x) = x^7 + 3x^4$?
5. Can you explain the product rule in differentiation?

Tip: Remember that the power rule applies only when the variable has a constant exponent!