We consider the problem of differentiating a multivariable function specified by noisy data. Following previous work for the single-variable case, we regularize the differentiation process, by formulating it as an inverse problem with an integration operator as the forward model. Total-variation regularization avoids the noise amplification of finite-difference methods, while allowing for discontinuous solutions. Unlike the single-variable case, we use an alternating directions, method of multipliers algorithm to provide greater efficiency for large problems. We apply the method to synthetic data and to synthetic-aperture radar satellite imagery.