If `y=3x^2+2x`, then find `dy//dx`.

Options

A. 6x-2
B. 6x
C. 6x+1
D. `6x+2`

Explanation

To find the derivative of the function \( y = 3x^2 + 2x \) with respect to \( x \), we will use the rules of differentiation.

### Step-by-step Solution:

1. **Identify the function**: We have the function \( y = 3x^2 + 2x \).

2. **Differentiate each term separately**:
- The first term is \( 3x^2 \).
- The second term is \( 2x \).

3. **Apply the power rule**: The power rule states that if \( y = ax^n \), then \( \frac{dy}{dx} = n \cdot ax^{n-1} \).
- For \( 3x^2 \):
- Here, \( a = 3 \) and \( n = 2 \).
- Applying the power rule:
\[ \frac{d}{dx}(3x^2) = 2 \cdot 3x^{2-1} = 6x. \]
- For \( 2x \):
- Here, \( a = 2 \) and \( n = 1 \).
- Applying the power rule:
\[ \frac{d}{dx}(2x) = 1 \cdot 2x^{1-1} = 2. \]

4. **Combine the results**: Now, we add the derivatives of both terms:
\[ \frac{dy}{dx} = 6x + 2. \]

5. **Final answer**: Thus, the derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 6x + 2. \]