Hamilton's principle
δ S = 0 {\displaystyle \delta S=0}
Functional Derivative
f → f + δ f {\displaystyle f\rightarrow f+\delta f} Expansion gives the first order term in δ f {\displaystyle \delta f} Then it is d F / d f {\displaystyle dF/df}
Expansion gives the first order term in 
Then it is 