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To solve the problem of finding the derivative of the function \( f(x) = x^2 + 3x + 2 \), we can apply the basic rules of differentiation.

### Steps:
1. **Differentiate each term**:
   - The derivative of \( x^2 \) with respect to \( x \) is \( 2x \).
   - The derivative of \( 3x \) with respect to \( x \) is \( 3 \).
   - The derivative of the constant \( 2 \) is \( 0 \).

2. **Combine the derivatives**:
   \[
   f'(x) = 2x + 3
   \]

### Conclusion:
The correct answer is **D. \( 2x + 3 \)**.

Would you like a detailed explanation or have any questions?

Here are 5 related questions to consider:
1. How do you find the derivative of a polynomial function in general?
2. What is the derivative of the function \( f(x) = 4x^3 + 2x^2 - 5x + 1 \)?
3. How does the power rule help in finding the derivative of any term like \( ax^n \)?
4. What is the geometric interpretation of the derivative \( f'(x) \)?
5. How does the derivative of a constant function compare to the derivative of a linear function?

**Tip:** When differentiating, always check if you need to apply any special rules (e.g., product rule, quotient rule, chain rule) depending on the complexity of the function.

Find the derivative of f(x) = x^2 + 3x + 2.

Explore how to find the derivative of the function f(x) = x^2 + 3x + 2 using basic rules of differentiation. This problem covers essential calculus concepts, including the power rule and differentiation of polynomial functions. Suitable for students in Grades 10-12.

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