Basic Differentiation: 
o Differentiate the following functions with respect to x: 
▪ f(x) = 3x2+2x+1 

To differentiate the function \( f(x) = 3x^2 + 2x + 1 \) with respect to \( x \), we apply the basic rules of differentiation.

### Function:
\[ f(x) = 3x^2 + 2x + 1 \]

### Step-by-step differentiation:

1. **Differentiate \( 3x^2 \):**
   \[
   \frac{d}{dx}(3x^2) = 3 \cdot 2x^{2-1} = 6x
   \]

2. **Differentiate \( 2x \):**
   \[
   \frac{d}{dx}(2x) = 2 \cdot 1x^{1-1} = 2
   \]

3. **Differentiate the constant \( 1 \):**
   \[
   \frac{d}{dx}(1) = 0
   \]

### Final result:
\[
f'(x) = 6x + 2
\]

The derivative of the function \( f(x) = 3x^2 + 2x + 1 \) is \( f'(x) = 6x + 2 \).

Would you like more details on how these rules work or have any other questions?

Here are 5 related questions for further exploration:

1. What is the derivative of \( g(x) = 5x^3 + 4x^2 + 3x + 2 \)?
2. How do we differentiate trigonometric functions like \( \sin(x) \)?
3. What is the second derivative of \( f(x) = 3x^2 + 2x + 1 \)?
4. How does the chain rule apply in differentiation?
5. What is the derivative of \( f(x) = e^x \)?

**Tip:** When differentiating powers of \( x \), apply the power rule: \( \frac{d}{dx}(x^n) = nx^{n-1} \).

Differentiate the following functions with respect to x: f(x) = 3x^2 + 2x + 1

Learn how to differentiate the polynomial function f(x) = 3x^2 + 2x + 1 using basic differentiation rules. This solution covers key calculus concepts like the power rule and sum rule, suitable for students in Grades 10-12.

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