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Re: Inversing derivative (NOT an inverse derivative!)
Posted:
Jan 16, 2013 3:54 PM
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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 text-books which
rigorously insist on f(x) and f'(x) all the time, denying students the
gift which Leibniz gave us.
Ken Pledger.
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