(D) $x 2+4 x+3$
\(\boxed{f'(x) = 2x + 4}\)
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 :\(\boxed{f'(x) = 2x + 4}\)