The sensitivity of capacitances to the design parameters can be computed either by the derivative of state variables (the derivative method) or by the adjoint variable method. This paper proposes a second order sensitivity computation method that combines the two methods in exploring the solutions of the derivative of state variables and of the adjoint variables. By using the variational method for the electric flux computation, it can be shown that the right hand side of the adjoint system is identical to the right hand side of the original system in capacitance matrix extraction. The computational complexity of the method is hence identical to that of the first order sensitivity using the derivative method, which is linear to the number of design parameters. The first and second order derivatives of the material matrix necessary in the implementation are obtained with the help of the first and second order local jacobian derivatives. The method is validated through an example of a comb-drive microelectromechanical system (MEMS).