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The derivative of the given function \( y = \frac{7}{(7 - x^6)^{\frac{3}{2}}} \) is:

\[
\frac{dy}{dx} = 63x^5(7 - x^6)^{- \frac{5}{2}}
\]

Would you like further explanation or more details on the steps involved?

Here are some related questions:
1. How do you apply the chain rule to functions like this one?
2. Can you explain why we needed to use the power rule for differentiation?
3. How can we simplify derivatives involving negative exponents?
4. What would happen if \(x = 0\) in this derivative?
5. How do second derivatives work for functions like this?

**Tip:** When differentiating, always check for composite functions, as they often require the chain rule for correct handling.

Find the derivative of y = 7 / (7 - x^6)^(3/2).

Learn how to differentiate y = 7 / (7 - x^6)^(3/2) using the chain rule and power rule. This solution covers key calculus concepts suitable for undergraduate students.

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