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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`
Wolfram Language code: <<VariationalMethods`

This is the first variational derivative of :

Version 5.2 VariationalD[y[x] Sqrt[1 + y'[x]^2], y[x], x]
Wolfram Language code: VariationalD[y[x] Sqrt[1 + y'[x] ^ 2], y[x], x]