To find the derivative of f(x) = 1/√x, we first rewrite it in power form as f(x) = x^(-1/2). Applying the power rule (d/dx [x^n] = n*x^(n-1)), we get f'(x) = (-1/2) * x^(-1/2 - 1) = (-1/2) * x^(-3/2) = -1 / (2 * x^(3/2)). Now, substitute x = 4: f'(4) = -1 / (2 * 4^(3/2)). Since 4^(3/2) = (√4)^3 = 2^3 = 8, the derivative is -1 / (2 * 8) = -1/16. Option B is incorrect due to the sign; options C and D represent incorrect power rule applications.