Numerical forward modeling, predicting an observable response given a mathematical representation of the Earth, is an important component of practical exploration work. In addition, derivatives which relate changes in response to changes in the Earth model are useful for experimental design and are a crucial element of linearized inversion techniques. Differentiation of kernels followed by numerical integration using a fast Hankel transform provides an efficient combination of forward and sensitivity modeling for frequency-domain horizontal electric dipole-dipole sounding over a layered seafloor. Our code is validated against an independent forward modeling technique using a mode analysis and against central difference derivatives. Efficiency is important in the application of regularized inversion to large data sets; we give an example from the East Pacific Rise, requiring 2000 elements in the Jacobian matrix. We illustrate the use of forward modeling and discrete analogs of the Fr¿chet kernels to provide aid to physical intuition and experimental design in the context of the electrical conductivity of the oceanic lithosphere. By using the most favorable parts of range-frequency space, experiments using current technology should be capable of distinguishing a thicker, less resistive, from a thinner, more resistive ''lithospheric resistor'' layer. ¿ American Geophysical Union 1996