  Derivative expansion and large-$D$ expansion are two perturbation techniques,
which are used to generate dynamical black-brane solutions to Einstein's
equations in presence of negative cosmological constant. In this note we have
compared these two techniques and established the equivalence of the gravity
solutions generated by these two different techniques in appropriate regime of
parameter space up to first non-trivial order in both the perturbation
parameters for Einstein-Maxwell systems, generalizing the earlier works of
[arXiv:1807.05058], [arXiv:1902.00854] for non-charged systems. An one-to-one
map between dynamical black-brane geometry and AdS space, which also exists at
finite number of dimensions, has also been established.
