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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.

Learn how to differentiate y = sin(4x) using the chain rule. The solution involves applying trigonometric and differentiation concepts, making it ideal for high school students studying calculus.

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