information:filtering, information:classification
The Laplacian

Another common generalization of the second derivative is the Laplacian. This is the differential operator ∇ 2 {\displaystyle \nabla ^{2}} (or Δ {\displaystyle \Delta }) defined by ∇ 2 f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2. {\displaystyle \nabla ^{2}f={\frac {\partial ^{2}f}{\partial x^{2}}}+{\frac {\partial ^{2}f}{\partial y^{2}}}+{\frac {\partial ^{2}f}{\partial z^{2}}}.} The Laplacian of a function is equal to the divergence of the gradient, and the trace of the Hessian matrix.