A new complex-variable version of a cohesive element is presented that provides highly accurate first order derivatives of the nodal displacements with respect to the cohesive fracture parameters. These sensitivities are provided as a byproduct of the analysis using the complex Taylor series expansion method. This information is useful for inversely determining the cohesive fracture parameters from experimental or synthetic data using a finite element-based approach. In particular, the PPR cohesive element (Park et al., 2009), was extended using complex variables as a user element for the well-known commercial finite element program, Abaqus. The source code for the element is provided as an educational resource. The advantage of having accurate first order derivatives on both accuracy and efficiency is demonstrated through numerical examples.