Abstract
We will show that the derivative as a map on classical function spaces of analysis is characterized by the Leibniz rule as well as the chain rule. This is a consequence of results in this and the next chapter. We first study the solutions of the Leibniz rule equation as a map on the k-times continuously differentiable functions Ck. There are many examples of derivations in algebra and differential geometry generalizing the Leibniz rule for the derivative of products of functions.
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König, H., Milman, V. (2018). The Leibniz Rule. In: Operator Relations Characterizing Derivatives . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-00241-1_3
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DOI: https://doi.org/10.1007/978-3-030-00241-1_3
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-00240-4
Online ISBN: 978-3-030-00241-1
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