DIFFERENTIALS OF FUNCTIONS OF A SINGLE VARIABLE

Dennis M. Cates ()

Chapter Chapter 4 in Cauchy's Calcul Infinitésimal, 2019, pp 17-20 from Springer

Abstract: Abstract Let $$y=f(x)$$ always be a function of the independent variable x, i an infinitely small quantity and h a finite quantity. If we set $$ i = \alpha h, $$ $$ \alpha $$ will also be an infinitely small quantity, and we will have identically $$\begin{aligned} \frac{f(x + i) - f(x)}{i} = \frac{f(x + \alpha h) - f(x)}{\alpha h}, \end{aligned}$$

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_4

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