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The problem asks for the derivative \( f'(x) \) of the function \( f(x) = \frac{1}{x^3} \).

### Step-by-Step Solution:

1. **Rewrite the function:**
   \[
   f(x) = \frac{1}{x^3} = x^{-3}
   \]

2. **Differentiate using the power rule:**
   The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).
   
   Applying this to \( f(x) = x^{-3} \):
   \[
   f'(x) = -3 \cdot x^{-4} = -\frac{3}{x^4}
   \]

### Conclusion:

The correct derivative is \( f'(x) = -\frac{3}{x^4} \), which corresponds to the second option in the list.

Would you like more details, or do you have any questions?

Here are 8 related questions you might find helpful:

1. What is the power rule for differentiation, and how is it applied?
2. How do you differentiate functions that are in the form of \( x^n \)?
3. What are the common mistakes when differentiating functions like \( f(x) = \frac{1}{x^n} \)?
4. How do you differentiate functions that involve negative exponents?
5. Can you explain the chain rule and when it is used?
6. How do you find higher-order derivatives of functions like \( f(x) = \frac{1}{x^3} \)?
7. How does differentiation relate to the concept of a tangent line?
8. What are the practical applications of finding derivatives in real-world scenarios?

**Tip:** Always simplify the function, if possible, before differentiating to make the process easier.

Learn how to differentiate the function f(x) = 1/x^3 with a detailed step-by-step solution. This problem covers differentiation using the power rule and is suitable for advanced high school students.

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