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The derivative of the function \( y = 10(6x^9 - 9x + 2)^{-8} \) is:

\[
\frac{dy}{dx} = \frac{720(1 - 6x^8)}{(6x^9 - 9x + 2)^9}
\]

Would you like further explanation on how this derivative was calculated?

Here are 5 related questions:
1. What are the general steps for finding the derivative of a function using the chain rule?
2. How can you differentiate more complex composite functions like the one in this example?
3. What role does simplifying the derivative play in solving calculus problems?
4. How does the chain rule apply to functions with multiple terms inside a power?
5. What happens to the derivative when the exponent of a function is negative?

**Tip:** When differentiating powers of composite functions, always apply the chain rule to handle both the outer and inner functions correctly.

Find the derivative of y = 10(6x^9 - 9x + 2)^{-8}.

This solution explains how to find the derivative of the function y = 10(6x^9 - 9x + 2)^{-8} using the chain rule and power rule. Perfect for students studying calculus and learning advanced differentiation techniques.

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