The del operator () is an operator commonly used in vector calculus to find derivatives in higher dimensions. When applied to a function of one independent variable, it yields the derivative. For multidimensional scalar functions, it yields the gradient. If either dotted or crossed with a vector field, it produces divergence or curl, respectively, which are the vector equivalents of differentiation.

There are six ways del can be used to compute second derivatives of multivariable functions.

  • The divergence of the gradient, also know as the Laplacian
  • The vector Laplacian, equal to the Laplacian of each component of the vector
  • The curl of the gradient, always equal to 0 (see irrotational vector field)
  • The gradient of the divergence
  • The divergence of curl, always equal to 0 (see incompressible vector field)
  • The curl of the curl
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