Computation of the effective action (Peskin 11.4)

[babamarysol]

The generating functional Z[J] depends on $$\phi_{cl}$$ trough its dependence on J. At the lowest order in perturbation theory the relation between J(x) and $$\phi_{cl}$$ is just the classical field equation:

$$\left(\frac{\delta L}{\delta \phi}\right)_{\phi=\phi_{cl}} + J(x) = 0$$

The question is simple: why this expression for the field equation?

Please help me

 

[babamarysol]

Ah that's ok it's a functional derivative...