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The Differentiation of a Function of a Function

Published online by Cambridge University Press:  03 November 2016

H. S. Carslaw
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Extract

If z is a function of y having a differential coefficient at a certain point, and y is a function of x having a differential coefficient at the corresponding point, then z is a function of x having a differential coefficient at that point, and this differential coefficient is given by the formula

This theorem, thought not always stated so carefully, will be found in all texts on the calculus; but, so far as I am aware, no English writer, not even the most exact, offers a valid proof.

Type
Research Article
Information
The Mathematical Gazette , Volume 12 , Issue 170 , May 1924 , pp. 92 - 95
Copyright
Copyright © Mathematical Association 1924

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References

page note 92 * A function is said to satisfy a certain condition in the neighbourhood of a point x=a, when there is a positive number h such that the condition is satisfied for all values of x from (a-h) to (a+h), i.e, when 0 < | x-a | ≦h, as a is usually excluded.