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The curious history of Faà di Bruno’s formula. (English) Zbl 1024.01010

Faà di Bruno published his formula concerning the \(m\)-th derivative of a composite function \(g(f(t))\) in December 1855. In the present paper it is pointed out that several other mathematicians found different expressions of the \(m\)-th derivative of \(g(f(t))\) in the 19th century. These are all independent of Faà di Bruno’s work and a few of them predate it. Faà di Bruno was neither the first to state the formula that bears his name, nor the first to prove it.

MSC:

01A55 History of mathematics in the 19th century
26-03 History of real functions
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
05A18 Partitions of sets
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