We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines. To tackle visibility-related derivatives that make rendering non-differentiable, existing physically based differentiable rendering methods often rely on elaborate guiding data structures or reparameterization with a global impact on variance. In this article, we investigate an alternative that embraces nonzero bias in exchange for low variance and architectural simplicity. Our method expands the lower-dimensional boundary integral into a thin band that is easy to sample when the underlying surface is represented by an SDF. We demonstrate the performance and robustness of our formulation in end-to-end inverse rendering tasks, where it obtains results that are competitive with or superior to existing work.