Differentiate the function.
f left parenthesis x right parenthesis equals x Superscript 9

To differentiate the function \( f(x) = x^9 \), we will use the power rule of differentiation. The power rule states:

\[
\frac{d}{dx} \left( x^n \right) = n x^{n-1}
\]

where \( n \) is a constant.

Applying the power rule to \( f(x) = x^9 \):

\[
f'(x) = 9x^{9-1} = 9x^8
\]

So, the derivative of \( f(x) = x^9 \) is:

\[
\boxed{f'(x) = 9x^8}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the derivative of \( f(x) = x^{10} \)?
2. How would you differentiate \( f(x) = x^9 + x^8 \)?
3. What is the second derivative of \( f(x) = x^9 \)?
4. Can you explain the power rule in more detail?
5. How do you differentiate functions that are products of different powers of \( x \)?

**Tip:** The power rule is a fundamental rule in calculus and is very useful for differentiating polynomial functions!

Learn how to differentiate the function f(x) = x^9 using the power rule of differentiation. This solution includes a step-by-step process, applying the formula d/dx (x^n) = n * x^(n-1). Suitable for students in Grades 11-12 or introductory calculus courses.

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