The given function is:

\[
f(x) = \frac{2}{5}x
\]

This is a linear function, where the coefficient of \(x\) is \(\frac{2}{5}\). To find the derivative of \(f(x)\) with respect to \(x\), we apply the basic rule for differentiating a linear function:

\[
f'(x) = \frac{d}{dx} \left( \frac{2}{5}x \right)
\]

The derivative of \(x\) with respect to \(x\) is 1, so the derivative of the function becomes:

\[
f'(x) = \frac{2}{5}
\]

Thus, the derivative of \(f(x) = \frac{2}{5}x\) is:

\[
f'(x) = \frac{2}{5}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the derivative of \(f(x) = ax\) for any constant \(a\)?
2. How does the derivative of a constant function compare to a linear function?
3. How do you find the derivative of a polynomial function like \(f(x) = 2x^2 + 5x + 1\)?
4. What does the derivative of a function tell us about the slope of the graph?
5. How does differentiating power functions like \(x^n\) differ from linear ones?

**Tip:** For linear functions, the derivative is always the coefficient of \(x\), which represents the constant rate of change.

Learn how to find the derivative of the linear function f(x) = 2/5x. This problem covers key calculus concepts such as derivatives and linear functions, with a detailed explanation. Suitable for students in Grades 10-12.

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