f(x) can be written as x^(1/2). Applying the power rule: d/dx(x^n) = n*x^(n-1), we get (1/2)*x^(1/2 - 1) = (1/2)x^(-1/2) = 1 / (2sqrt(x)). Option B is the reciprocal. Option C is missing the factor of 1/2. Option D incorrectly includes a negative sign.