We suggest a plasmonic nanodevice for performing the second-order spatial derivative of light fields. The device consists of five gold nanorods arranged to evanescently couple to each other so that emit cross-polarized output proportional to the second-order differentiation of the incident wave. A theoretical model based on the electrostatic eigenmode analysis is derived and numerical simulations using the finite-difference time-domain methods are provided as supporting evidence. It is shown in both the analytic and numerical methods that the proposed plasmonic circuit performs second-order differentiation of the phase of the incident light field in transmission mode with a subwavelength planar resolution. The resolution of 0.29 λ-1 is numerically demonstrated for a 20 nm thick circuit at the wavelength of 700 nm. The suggested plasmonic device has potential application in miniaturized systems for all-optical computation.