The derivative of `f (x) = x^(2) + 2x` at `x = 2` is

Options

A. 10
B. 12
C. 14
D. 16

Answer

To find the derivative of the function \( f(x) = x^2 + 2x \) at \( x = 2 \), we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating the function \( f(x) \) with respect to \( x \).

\[ f'(x) = \frac{d}{dx}(x^2 + 2x) \]

### Step 2: Apply the power rule
Using the power rule of differentiation, which states that \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \), we differentiate each term:

1. The derivative of \( x^2 \) is \( 2x \).
2. The derivative of \( 2x \) is \( 2 \).

So, we have:

\[ f'(x) = 2x + 2 \]

### Step 3: Evaluate the derivative at \( x = 2 \)
Now, we need to find the value of the derivative at \( x = 2 \):

\[ f'(2) = 2(2) + 2 \]

Calculating this gives:

\[ f'(2) = 4 + 2 = 6 \]

### Final Answer
Thus, the derivative of \( f(x) \) at \( x = 2 \) is:

\[ \boxed{6} \]

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