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Topic: Inversing derivative (NOT an inverse derivative!)
Replies: 3   Last Post: Jan 16, 2013 7:23 PM

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 Ken.Pledger@vuw.ac.nz Posts: 1,412 Registered: 12/3/04
Re: Inversing derivative (NOT an inverse derivative!)
Posted: Jan 16, 2013 3:54 PM

In article <1852d6e6f1f3cfb205836af0e8bd9dc3@breaka.net>,

> Keeping in mind df(x)/dx = f'(x), if y'(x) = 1/x'(y) and,
> likewise, x'(y) = 1/y'(x), how do you express 1/y'(x)
> in terms of "d"?
> Is it just dx/dy(x) ....

Leibniz was very concerned about good notation. He tried and
discarded various notations before settling on the d and long s. One of
the beautiful mnemonics built into that notation is dx/dy = 1/(dy/dx).
It looks just like manipulating an algebraic fraction, although of
course it's actually deeper. The same goes for the chain rule dz/dx =
(dz/dy)(dy/dx), and the rule for integration by substitution ("cancel
the dx").

It's always sad to see elementary calculus text-books which
rigorously insist on f(x) and f'(x) all the time, denying students the