It looks like you're asking to differentiate an expression that involves two functions, possibly \(\frac{x^2}{9 - x^2}\), but the formatting is unclear. If this is the case, you're seeking the derivative of:

\[
f(x) = \frac{x^2}{9 - x^2}
\]

### Steps to Differentiate:

1. **Apply the Quotient Rule**: For \(\frac{u(x)}{v(x)}\), the derivative is:
   \[
   \frac{d}{dx}\left(\frac{u(x)}{v(x)}\right) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}
   \]

2. **Identify the components**:
   - \( u(x) = x^2 \), so \( u'(x) = 2x \)
   - \( v(x) = 9 - x^2 \), so \( v'(x) = -2x \)

3. **Apply the Quotient Rule**:
   \[
   \frac{d}{dx} \left(\frac{x^2}{9 - x^2}\right) = \frac{(2x)(9 - x^2) - (x^2)(-2x)}{(9 - x^2)^2}
   \]

4. **Simplify the result**:
   \[
   = \frac{2x(9 - x^2) + 2x^3}{(9 - x^2)^2}
   \]
   \[
   = \frac{18x - 2x^3 + 2x^3}{(9 - x^2)^2}
   \]
   \[
   = \frac{18x}{(9 - x^2)^2}
   \]

Thus, the derivative of \(\frac{x^2}{9 - x^2}\) is:

\[
f'(x) = \frac{18x}{(9 - x^2)^2}
\]

Let me know if you'd like more details on any step, or if you need clarification!

### Relative Questions:
1. What is the Quotient Rule and when is it used?
2. How do you find the derivative of \(x^2\)?
3. What is the derivative of \(9 - x^2\)?
4. Can you explain how to simplify expressions with fractions?
5. What are some common mistakes when applying the Quotient Rule?

**Tip**: Always double-check whether the Quotient Rule or the Product Rule applies by identifying the form of the expression you're differentiating.

Learn how to differentiate the function x^2/(9 - x^2) using the Quotient Rule. This step-by-step guide explains key calculus concepts like the Quotient Rule and simplifies the result. Suitable for advanced high school or college students.

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