A targeted {AD} approach is presented to calculate directional second order derivatives of ODE/DAE embedded functionals accurately and eficiently. This advance enables us to tackle the solution of large scale dynamic optimization problems using a truncated-Newton method where the Newton equation is solved approximately to update the direction for the next optimization step. The proposed directional second order adjoint method ({dSOA}) provides accurate Hessian-vector products for this algorithm. The implementation of the ‘‘{dSOA} powered’’ truncated- Newton method for the solution of large scale dynamic optimization problems is showcased with an example.