gateaux derivative of one functional

fenglingchao

The functional is given as follows,
[itex]\phi(\theta)(t)=t\cdot \theta (t^{1/(I-1)})[/itex]
where [itex]I\geq 2[/itex] is a constant.

We need to get the gateaux derivative of the functional [itex]\phi[/itex]. Thanks.