  Using the one-loop Coleman-Weinberg effective potential, we derive a general
analytic expression for all the derivatives of the effective potential with
respect to any number of classical scalar fields. The result is valid for a
renormalisable theory in four dimensions with any number of scalars, fermions
or gauge bosons. This result corresponds to the zero-external momentum
contribution to a general one-loop diagram with N scalar external legs. We
illustrate the use of the general result in two simple scalar singlet
extensions of the Standard Model, to obtain the dominant contributions to the
triple couplings of light scalar particles under the zero external momentum
approximation
