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On certain formulae for Repeated Differentiation

Published online by Cambridge University Press:  20 January 2009

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In many questions of analysis relating to the theory of plane curves, it is convenient to be able to obtain quickly the expansions of and of These may be obtained as follows:—

By an obvious extension of the theorem of Leibnitz we have

where d 1,d 2,…d n differentiate y 1, y 2,…y n respectively.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1884