Discussion:
differentiation from first principles
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sean doyle
2008-02-05 13:49:54 UTC
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Tried without success to differentiate 1/x from first principles using delta
x, can anyone help?
Virgil
2008-02-05 18:20:26 UTC
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Post by sean doyle
Tried without success to differentiate 1/x from first principles using delta
x, can anyone help?
Using h instead of delta x: and assuming x is not 0

[1/(x+h) - 1/x]/h = [(x - (h+h))/(x*(x+h))]/h
= [-h/(x*(x+h)]/h
= -1/(x*(x+h))
--> -1/x^2 as h --> 0
Ken Pledger
2008-02-06 23:47:17 UTC
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....
[1/(x+h) - 1/x]/h = [(x - (h+h))/(x*(x+h))]/h ....
Just in case it confused the OP, I'll mention the typo:

(x - (h+h)) should have been (x - (x+h)).

Ken Pledger.
Virgil
2008-02-07 01:16:16 UTC
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Post by Ken Pledger
....
[1/(x+h) - 1/x]/h = [(x - (h+h))/(x*(x+h))]/h ....
(x - (h+h)) should have been (x - (x+h)).
Ken Pledger.
Thanks!

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