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### Problem Overview:
The problem asks to find the functions \( f \cdot g \), \( f + g \), \( f - g \), and \( \frac{f}{g} \) for given functions \( f(x) \) and \( g(x) \), and then find their derivatives.

### Given Functions:
1. **First set:**
   - \( f(x) = x^3 + 2x^2 \)
   - \( g(x) = 3x^2 - 1 \)

2. **Second set:**
   - \( f(x) = \sqrt{1 + x^2} \)
   - \( g(x) = \frac{1}{1 + x^2} \)

3. **Third set:**
   - \( f(x) = x^2 \)
   - \( g(x) = \frac{1}{x^2} \)

### Task:
For each pair of functions:
1. Compute the following:
   - \( f \cdot g \)
   - \( f + g \)
   - \( f - g \)
   - \( \frac{f}{g} \)
2. Compute the derivative of each of the above functions.

Would you like to proceed with solving all these tasks, or is there a specific part you would like to focus on first?

Find functions f⋅g, f+g, f−g, and f/g and find their derivatives for the following sets of functions:
1) f(x) = x^3 + 2x^2, g(x) = 3x^2 - 1
2) f(x) = sqrt(1 + x^2), g(x) = 1/(1 + x^2)
3) f(x) = x^2, g(x) = 1/x^2

This exercise involves finding the functions f⋅g, f+g, f−g, and f/g for three pairs of functions and computing their derivatives. This task demonstrates the application of differentiation rules including the product rule, sum rule, and quotient rule. Suitable for high school students in Grades 11-12.

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