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.