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Re: Inversing derivative (NOT an inverse derivative!)
Posted:
Jan 16, 2013 3:54 PM


In article <1852d6e6f1f3cfb205836af0e8bd9dc3@breaka.net>, Anonymous <noreply@breaka.net> wrote:
> 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 textbooks which rigorously insist on f(x) and f'(x) all the time, denying students the gift which Leibniz gave us.
Ken Pledger.



