# What is the derivative of 1/3x?

#### Understand the Problem

The question is asking for the derivative of the function 1/3x, which involves applying the rules of differentiation to find the rate of change of the function with respect to x.

#### Answer

The derivative of the function is $f'(x) = \frac{1}{3}$.
##### Answer for screen readers

The derivative of the function $f(x) = \frac{1}{3}x$ is $f'(x) = \frac{1}{3}$.

#### Steps to Solve

1. Identify the function to differentiate We are given the function $f(x) = \frac{1}{3}x$.

2. Apply the power rule The power rule states that if $f(x) = ax^n$, then the derivative $f'(x) = nax^{n-1}$. Here, we can rewrite $f(x)$ as $\frac{1}{3} \cdot x^1$.

3. Differentiate using the power rule Using the power rule, we find the derivative: $$f'(x) = 1 \cdot \frac{1}{3} x^{1-1} = \frac{1}{3} x^0 = \frac{1}{3}$$

4. Write the final answer The derivative of the function is simply the constant we calculated.

The derivative of the function $f(x) = \frac{1}{3}x$ is $f'(x) = \frac{1}{3}$.

#### More Information

The derivative represents the slope of the function at any point, and since our derivative is a constant, it indicates that the function has a constant rate of change.

#### Tips

• A common mistake is forgetting to apply the power rule correctly, especially with the exponent.
• Another mistake might be neglecting to simplify the expression appropriately.
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