https://file.aiquickdraw.com/mathbot/file/1729295606978mnknom63.jpg

The given function is:

\[
y = \left( 5x + \left( 9x + \arcsin(7x) \right)^6 \right)^5
\]

Would you like to find the derivative \(\frac{dy}{dx}\) or explore something else with this equation? Let me know how you'd like to proceed.

Here are a few related questions:
1. Would you like to simplify or expand the expression?
2. Do you want to find the critical points of this function?
3. Would you prefer to evaluate this function at specific values of \(x\)?
4. Are you interested in the behavior of this function as \(x \to 0\) or \(x \to \infty\)?
5. Would you like to analyze the domain and range of this function?

**Tip**: When differentiating composite functions like this, applying the chain rule carefully is essential.

Learn how to differentiate the complex composite function y = (5x + (9x + arcsin(7x))^6)^5. This problem involves using the chain rule, the power rule, and the derivative of the inverse sine function. Suitable for students in Grades 11-12 and college-level calculus.

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