Upgrading from:

Calculus`VariationalMethods`

All the functionality in Calculus`VariationalMethods` is now available through the newly created Variational Methods Package.

To access functionality from the new Variational Methods Package, load VariationalMethods`:

Version 5.2 << Calculus`VariationalMethods`

This is the first variational derivative of :

Version 5.2 VariationalD[y[x] Sqrt[1 + y'[x]^2], y[x], x]