The derivative of f(x)=`3x^2` +2x + 4 w.r.t. x is

Options

A. `3(6x+2)^2`
B. `6x+ 4`
C. `3(2x + 3)`
D. `6x + 2`

Answer

To find the derivative of the function \( f(x) = 3x^2 + 2x + 4 \) with respect to \( x \), we will follow these steps:

### Step 1: Identify the function
We have the function:
\[ f(x) = 3x^2 + 2x + 4 \]

### Step 2: Apply the differentiation rules
We will use the power rule of differentiation, which states that:
\[ \frac{d}{dx}(x^n) = n \cdot x^{n-1} \]

### Step 3: Differentiate each term
1. Differentiate \( 3x^2 \):
- Using the power rule, we get:
\[ \frac{d}{dx}(3x^2) = 3 \cdot 2x^{2-1} = 6x \]

2. Differentiate \( 2x \):
- Again using the power rule, we have:
\[ \frac{d}{dx}(2x) = 2 \cdot 1x^{1-1} = 2 \]

3. Differentiate the constant \( 4 \):
- The derivative of any constant is \( 0 \):
\[ \frac{d}{dx}(4) = 0 \]

### Step 4: Combine the results
Now, we combine the derivatives of each term:
\[ \frac{d}{dx}(f(x)) = 6x + 2 + 0 \]

### Step 5: Write the final answer
Thus, the derivative of the function \( f(x) \) with respect to \( x \) is:
\[ f'(x) = 6x + 2 \]