Hi,

First post so be gentle!

I'm trying to find the Gateaux Differential for the following:

Given the functional:

S[y]=\cosh(T[y]), T[y]=\int_1^3(5\frac{dy}{dx}-2y^2)dx

I have to find the Gateaux Differential. Now, I'm comfortable with finding the Gateaux Differential for T[y] but my daft question is, for S[y] do I need to substitute T[y] into S[y] before generating the Gateaux Differential or do I find the Gateaux Differential of T[y] first and then substitute into S[y] ?

Any advice appreciated