This problem set asks for finding the derivative $\frac{dy}{dx}$ for each function listed. I'll go through the solutions for a few examples and then let you confirm if you'd like the full breakdown for each question.

Here are step-by-step solutions for the first few problems:

1. For $y = 2x^2 - 4x^2 + 7x - 5$:

   • Simplify the function first, if necessary.
   • Differentiate each term with respect to $x$: $\frac{dy}{dx} = 4x - 8x + 7 = -4x + 7.$

2. For $y = 9 - 3x^{-1} + 6x^{-2}$:

   • Differentiate each term: $\frac{dy}{dx} = 0 + 3x^{-2} - 12x^{-3} = \frac{3}{x^2} - \frac{12}{x^3}.$

3. For $y = (x^2 - x)(2x - 6)$:

   • Use the product rule: $y = u \cdot v$, where $u = x^2 - x$ and $v = 2x - 6$.
   • Differentiate $u$: $\frac{du}{dx} = 2x - 1$.
   • Differentiate $v$: $\frac{dv}{dx} = 2$.
   • Apply the product rule: $\frac{dy}{dx} = (x^2 - x) \cdot 2 + (2x - 6) \cdot (2x - 1).$

Would you like detailed solutions for all 17 questions, or are there specific questions you need help with?

Here are 5 related questions that build upon differentiation and help reinforce these concepts:

1. How do you apply the product rule for differentiation?
2. What steps do you follow when using the quotient rule in differentiation?
3. How does the power rule apply to negative exponents?
4. Why is it important to simplify a function before differentiating?
5. What are some common errors to avoid in differentiation, especially with complex fractions?

Tip: Always simplify the function as much as possible before differentiating—it often makes the calculations easier.