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The problem asks to find the derivative of the function \( f(x) = -\frac{1}{3}x \).

### Solution:
Given the function:
\[ f(x) = -\frac{1}{3}x \]

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

\[ f'(x) = \frac{d}{dx}\left(-\frac{1}{3}x\right) \]

The derivative of \( -\frac{1}{3}x \) with respect to \( x \) is \( -\frac{1}{3} \), because:

\[ \frac{d}{dx}\left(-\frac{1}{3}x\right) = -\frac{1}{3} \]

### Answer:
The correct answer is \(-\frac{1}{3}\).

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Would you like further clarification on this problem? Here are some related questions:

1. What is the general rule for differentiating a linear function?
2. How does the derivative change when the slope of the line changes?
3. Can the derivative of a linear function ever be zero?
4. What is the significance of the sign of the derivative?
5. How do you find the derivative of a function that includes both a constant and a variable term?
6. What does the derivative tell you about the graph of a function?
7. How do you apply the power rule to a function with a fractional coefficient?
8. What is the derivative of a function in the form \( ax + b \)?

**Tip:** When dealing with the derivative of a linear function, the derivative will always be the constant coefficient of \(x\).

Learn how to find the derivative of the function f(x) = -1/3x step-by-step with detailed explanations. This problem covers differentiation, derivatives of linear functions, and their applications. Suitable for high school students.

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