I explained that the idea of the derivative as an instantaneous rate of change actually predated both Newton and Leibniz, but the approach had an anomaly. We shared the old approach on the Elmo and I showed her the anomaly and then explained how Newton and Leibniz developed the concept of a limit and thus "cured" the anomaly. We did a sidebar consisting of some more calculus to determine the length of the rope between the goat and the railroad tie.