Let f:n be a C1(n) function, that is, a partially differentiable function in all its coordinates. The symbol , named nabla, represents the gradient operator, whose action on f(x1,x2,,xn) is given by

f = (fx1,fx2,,fxn)
= (fx1,fx2,,fxn)


  1. 1.

    If f,g are functions, then

  2. 2.

    For any scalars α and β and functions f and g,


The symbolism

Using the formalism, the divergence operator can be expressed as , the curl operator as ×, and the Laplacian operator as 2. To wit, for a given vector field


and a given function f we have

𝐀 =Axx+Ayy+Azz
×𝐀 =(Azy-Ayz)𝐢+(Axz-Azx)𝐣+(Ayx-Axy)𝐤
2f =2fx2+2fy2+2fz2.
Title nabla
Canonical name Nabla
Date of creation 2013-03-22 14:00:20
Last modified on 2013-03-22 14:00:20
Owner stevecheng (10074)
Last modified by stevecheng (10074)
Numerical id 7
Author stevecheng (10074)
Entry type Definition
Classification msc 26A06
Related topic gradient
Related topic NablaActingOnProducts
Related topic Gradient
Related topic AlternateCharacterizationOfCurl