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The image contains seven differentiation problems under "Activity 3: Skill-building Activities." Here's a breakdown of each question:

1. \( y = \frac{5}{x^3} - \frac{4}{x^2} + 10 \)
   - Differentiate with respect to \( x \).

2. \( y = \frac{x(2x+1)}{3x-5} \)
   - Use quotient and product rules to differentiate.

3. \( y = (x)(2x+1)(3x-5) \)
   - Apply product and chain rules to differentiate.

4. \( y = (4x^3 - 3x^2 - x - 5)^3 \)
   - Differentiate using the chain rule.

5. \( y = \sqrt{x^3 - 4x + 1} \)
   - Differentiate and find \( \frac{dy}{dx} \).

6. \( y = \left(\frac{x - 2}{x^2}\right)^3 \)
   - Use three methods to differentiate (product, quotient, binomial expansion).

7. \( y = (3x+1)^3(2x-3)^4 \)
   - Apply the product and chain rules.

Would you like detailed step-by-step solutions for each of these problems, or is there a specific one you'd like me to start with?

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Here are 5 relative questions to expand on differentiation concepts:
1. How does the product rule apply to more than two functions?
2. Can you derive the chain rule from first principles?
3. What are some common mistakes when applying the quotient rule?
4. How do higher-order derivatives impact the shape of a curve?
5. Why is implicit differentiation useful in solving certain problems?

**Tip:** Always check if the functions can be simplified before differentiating, as it can make the process easier.

Differentiate the following functions:
1. y = 5/x^3 - 4/x^2 + 10
2. y = x(2x+1)/(3x-5)
3. y = (x)(2x+1)(3x-5)
4. y = (4x^3 - 3x^2 - x - 5)^3
5. y = sqrt(x^3 - 4x + 1)
6. y = (x - 2)^3 / (x^2)^3
7. y = (3x+1)^3(2x-3)^4

Learn how to differentiate complex functions involving the quotient rule, product rule, and chain rule with these skill-building activities. The problems cover functions like y = (3x+1)^3(2x-3)^4 and y = sqrt(x^3 - 4x + 1), suitable for undergraduate students.

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