Definitions related to numerical derivatives | Quick start: reproducing the numDeriv vignette | Vectorisation pitfalls | Breakdown of numDeriv::grad | Handling vectorised inputs | Approximation method | Compatibility implies syntax support, not identical values | numDeriv zero handling has a discontinuity | Not all evaluations matter for Richardson extrapolation | Diagnostics | Higher-order accuracy diagnostics | References

Kernel methods | Fixed bandwidth | Rank weights | Nearest-neigbour weights | Simulation in 1 dimension | Simulation in 3 dimensions | Conclusion | References

Data-driven step-size selection procedures | Curtis--Reid (1974) bounded ratio approach | Dumontet--Vignes (1977) plug-in approach | Stepleman--Winarsky (1979) accurate-digit count estimation | Mathur (2012) AutoDX algorithm | Robust grid search | Not letting intermediate values go to waste | Non-uniform grid spacing | First-order derivatives | References

Introduction | Derivative approximation via finite differences | Derivatives from Taylor series | Derivatives on arbitrary stencils | Precision loss on computers | Numerical derivatives of scalar functions | Two-sided derivatives | One-sided derivatives | Second derivatives | Higher derivatives | Fourth-order-accurate derivatives | General derivative and accuracy orders | Cross-derivatives | Gradients, Jacobians, and Hessians | Numerical gradients | Numerical Jacobians | Numerical Hessians and cross-derivatives | Exploiting the Hessian symmetry | Derivatives from existing function values | Common issues with numerical derivatives | Stencil choice | Handling very small and very large arguments | Derivatives of noisy functions | Accuracy loss due to repeated differencing | Complex derivatives | TODO -- Uncategorised | References

Kernel methods | Speed-ups | Univariate kernel estimation | Multivariate kernel estimation | Sparsity | Conclusion | References