Seppo Linnainmaa automatic differentiation differentiable backpropagation chain rule Gottfried Wilhelm Leibniz Henry J. Kelley backpropagation control theory Paul Werbos backpropagation David E. Rumelhart
In 1970, Seppo Linnainmaa published the reverse mode of automatic differentiation of discrete connected networks of nested differentiable functions. This became known as backpropagation. It is an efficient application of the chain rule derived by Gottfried Wilhelm Leibniz in 1673 to networks of differentiable nodes. 
The terminology "back-propagating errors" was actually introduced in 1962 by Rosenblatt, but he did not know how to implement this, although Henry J. Kelley had a continuous precursor of backpropagation already in 1960 in the context of control theory. In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard. In 1985, David E. Rumelhart et al. published an experimental analysis of the technique.
