It seems like there is a typo in the function you've provided. I assume you meant to write \( f(x) = 9x^2 - x^3 \). I'll proceed with finding the derivative of this function.

The function is:
\[
f(x) = 9x^2 - x^3
\]

To find the derivative \( f'(x) \), we differentiate each term of the function with respect to \( x \):

1. The derivative of \( 9x^2 \) is \( 18x \).
2. The derivative of \( -x^3 \) is \( -3x^2 \).

So, the derivative of the function is:
\[
f'(x) = 18x - 3x^2
\]

Would you like any details or have any questions?

Here are 5 related questions for further practice:
1. What is the derivative of \( f(x) = 5x^3 + 2x^2 - x \)?
2. Find the second derivative of \( f(x) = 9x^2 - x^3 \).
3. Calculate the derivative of \( g(x) = x^4 - 4x^2 + 7 \).
4. What is the slope of the tangent line to the curve \( f(x) = 9x^2 - x^3 \) at \( x = 2 \)?
5. Find the critical points of \( f(x) = 9x^2 - x^3 \).

**Tip:** Always check your function for typos or errors before differentiating, as a small mistake can change the entire solution!

Discover how to find the derivative of the polynomial function f(x) = 9x^2 - x^3. This problem involves applying the power rule of differentiation to each term and is suitable for students in Grades 10-12 studying calculus.

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