The derivative of $y = \sin(4x)$ with respect to $x$ is:

$\frac{dy}{dx} = 4 \cos(4x)$

Would you like further details on this differentiation, or do you have any additional questions?

Here are five related questions to expand on this topic:

1. What is the second derivative of $y = \sin(4x)$?
2. How do you find the critical points of $y = \sin(4x)$?
3. Can you explain how to use the chain rule in differentiation?
4. What is the period of the function $y = \sin(4x)$?
5. How does the amplitude of $\sin(4x)$ compare to $\sin(x)$?

Tip: When differentiating trigonometric functions, remember to apply the chain rule if there is a constant multiplier inside the function.