If `f(x)=x^2+2x+7` , find `f\ '\ (3)` .

Explanation

To find \( f'(3) \) for the function \( f(x) = x^2 + 2x + 7 \), we will follow these steps:

### Step 1: Differentiate the function
We need to find the derivative \( f'(x) \). The function is composed of three terms: \( x^2 \), \( 2x \), and \( 7 \). We will differentiate each term separately.

1. The derivative of \( x^2 \) is \( 2x \) (using the power rule \( \frac{d}{dx}(x^n) = nx^{n-1} \)).
2. The derivative of \( 2x \) is \( 2 \) (since the derivative of \( x \) is \( 1 \)).
3. The derivative of \( 7 \) is \( 0 \) (since the derivative of a constant is \( 0 \)).
...