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It looks like you've uploaded a set of equations. Here's a breakdown of each one for differentiation or further analysis:

1. **Equation 9**: \( y = \sec(2x^4) \)
2. **Equation 10**: \( f(x) = (-3x^3 - 1)\csc(5x^4) \)
3. **Equation 11**: \( f(x) = \cos(3x^2) \cdot \sqrt[3]{5x^3 - 1} \)
4. **Equation 12**: \( f(x) = \sin(4x^3) \)
5. **Equation 13**: \( f(x) = \frac{4x^4 + 5}{\tan(3x^5)} \)
6. **Equation 14**: \( y = \cot\left(\sqrt[3]{5x^3 - 2}\right) \)

Would you like to compute the derivatives of any of these functions? If so, let me know which ones, and I can provide step-by-step explanations!

Here are 5 related questions to deepen your understanding:
1. How do we differentiate trigonometric functions involving powers, such as in Equation 9?
2. What rule should be applied when differentiating a product of two functions, as seen in Equation 10?
3. How do we apply the chain rule for Equation 11, which involves both trigonometric and radical expressions?
4. In Equation 12, what is the significance of the chain rule when dealing with composite functions?
5. Can you explain the role of the quotient rule in Equation 13?

**Tip**: When differentiating complex expressions involving products, quotients, or trigonometric functions, always identify whether you need to apply the chain, product, or quotient rule first!

Differentiate the following trigonometric and algebraic functions:
1. y = sec(2x^4)
2. f(x) = (-3x^3 - 1)csc(5x^4)
3. f(x) = cos(3x^2) * (5x^3 - 1)^(1/3)
4. f(x) = sin(4x^3)
5. f(x) = (4x^4 + 5)/tan(3x^5)
6. y = cot((5x^3 - 2)^(1/3))

This problem involves differentiating complex trigonometric and algebraic functions, including sec, csc, and cot, as well as radicals and composite functions. Key calculus concepts such as the chain, product, and quotient rules are applied. Suitable for advanced high school or introductory college-level calculus students.

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