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The given function is:

\[
y = 3 \arcsin(x^8) + 7 \arctan(3x)
\]

Would you like to compute the derivative of this function, evaluate it for specific values of \(x\), or explore other aspects of it? Let me know how you'd like to proceed!

Here are 5 related questions to expand on this:

1. What are the domains of \(\arcsin(x^8)\) and \(\arctan(3x)\)?
2. Would you like to compute the derivative \( \frac{dy}{dx} \) of this function?
3. Do you want to explore the behavior of the function for specific values of \(x\)?
4. How does the function behave as \(x \to 0\) or \(x \to \infty\)?
5. Would you like to analyze the inverse of this function?

**Tip**: Remember that the domain of \(\arcsin(x)\) is restricted to \([-1, 1]\), so the term \(\arcsin(x^8)\) implies specific restrictions on \(x\).

What is the behavior or derivative of the function y = 3 arcsin(x^8) + 7 arctan(3x)?

Explore the behavior and derivative of the function y = 3 arcsin(x^8) + 7 arctan(3x). This problem involves inverse trigonometric functions and uses the chain rule to find the derivative. Ideal for advanced high school or undergraduate students.

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