  We show that the effective actions of D-brane and M-brane are solutions to
the Hamilton-Jacobi (H-J) equations in supergravities. This fact means that
these effective actions are on-shell actions in supergravities. These solutions
to the H-J equations reproduce the supergravity solutions that represent
D-branes in a $B_2$ field, M2 branes and the M2-M5 bound states. The effective
actions in these solutions are those of a probe D-brane and a probe M-brane.
Our findings can be applied to the study of the gauge/gravity correspondence,
especially the holographic renormalization group, and a search for new
solutions of supergravity.
