The derivative of the function $f(x) = \frac{-2}{(3x + 4)^2}$ with respect to $x$ is:

$f'(x) = \frac{12}{(3x + 4)^3}$

Would you like more details on how this derivative was calculated, or do you have any questions?

Here are 5 related questions:

1. How do you find the derivative of a function that involves a chain rule?
2. What are the applications of derivatives in real-world scenarios?
3. How would the derivative change if the exponent in the denominator were different?
4. Can you explain the importance of understanding the derivative in calculus?
5. How does the derivative affect the graph of a function?

Tip: Always remember to simplify the expression as much as possible after finding the derivative to make it easier to interpret or use.