To find the derivative of the function \( f(x) = \frac{2}{x^2} \), we can rewrite the function in a more convenient form for differentiation:

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

Now, use the power rule for differentiation, which states:

\[
\frac{d}{dx}(x^n) = n \cdot x^{n-1}
\]

Applying this to \( 2x^{-2} \):

\[
f'(x) = 2 \cdot (-2) \cdot x^{-3} = -4x^{-3}
\]

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

\[
f'(x) = -\frac{4}{x^3}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the derivative change if \( f(x) = \frac{2}{x^n} \) for any \( n \)?
2. What is the second derivative of \( f(x) = \frac{2}{x^2} \)?
3. How does the graph of \( f(x) = \frac{2}{x^2} \) compare to its derivative?
4. What is the derivative of \( f(x) = \frac{2}{x^2} + 3x \)?
5. Can you integrate \( f'(x) = -\frac{4}{x^3} \) to recover \( f(x) \)?

**Tip:** When dealing with rational functions, it is often helpful to rewrite them as powers of \( x \) to make differentiation easier.

Learn how to find the derivative of the function f(x) = 2/x^2 using the power rule for differentiation. This solution covers key calculus concepts such as differentiating rational functions and applying the power rule. Suitable for advanced high school or early college students.

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