## Gateaux Differential

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 $S[y]$ ?