This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

VariationalD

VariationalD[f, u[x], x]
returns the variational derivative of the integral ∫fⅆx with respect to u[x], where the integrand f is a function of u, its derivatives, and x.
VariationalD[f, u[x, y, ...], {x, y, ...}]
returns the variational derivative of the multiple integral fxy ... with respect to u[x, y, ...], where f is a function of u, its derivatives and the coordinates x, y, ....
VariationalD[f, {u[x, y, ...], v[x, y, ...], ...}, {x, y, ...}]
gives a list of variational derivatives with respect to u, v, ....
Needs["VariationalMethods`"]
Variational derivative for the arc length ∫ⅆs of a plane curve:
In[2]:=
Click for copyable input
Out[2]=
 
Needs["VariationalMethods`"]
Variational derivative for the Dirichlet integral in two variables:
In[2]:=
Click for copyable input
Out[2]=