(D) $x 2+4 x+3$

Step 1 ：Given the function \(f(x) = x^2 + 4x + 3\)

Step 2 ：Apply the power rule for differentiation: \(f'(x) = nx^{n-1}\)

Step 3 ：Derivative of \(x^2\) is \(2x^{2-1} = 2x\)

Step 4 ：Derivative of \(4x\) is \(4x^{1-1} = 4\)

Step 5 ：Derivative of \(3\) is \(0\)

Step 6 ：Combine the derivatives: \(f'(x) = 2x + 4\)

Step 7 ：\(\boxed{f'(x) = 2x + 4}\)