Using a novel nonlinear time-variant transformation, we construct an explicit form of nonlinear consensus protocol that achieves dynamic consensus in multi-agent systems. A distinguishing feature of our protocol is that, under mild assumptions, exponential convergence is preserved from the consensus protocol in the original coordinates. Hence, consensus with switching graphs and large coupling delays, or consensus on general functions can be achieved if the protocol in the original coordinates does. Similar results are still rare in literature for nonlinear dynamics.