The function you provided is:

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

To find the derivative \( f'(x) \), we can rewrite the function as:

\[
f(x) = 2x^{-1}
\]

Now, apply the power rule of differentiation, which states that the derivative of \(x^n\) is \(n \cdot x^{n-1}\). For \(2x^{-1}\), the derivative is:

\[
f'(x) = 2 \cdot (-1) \cdot x^{-2} = -\frac{2}{x^2}
\]

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

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

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the derivative of \( f(x) = \frac{5}{x} \)?
2. How do you find the derivative of a quotient of two functions?
3. Can you explain the product rule for derivatives?
4. What is the second derivative of \( f(x) = \frac{2}{x} \)?
5. How would you integrate \( f(x) = \frac{2}{x} \)?

**Tip:** Rewriting functions in terms of exponents often makes differentiation easier.

Learn how to find the derivative of f(x) = 2/x using the power rule. This step-by-step solution explains key calculus concepts such as the power rule and differentiation. Ideal for students in Grades 11-12 studying calculus.

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