differentiation from first principles

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4 total messages Started by sean�doyle Tue, 05 Feb 2008 13:49

#99

Author: sean�doyle
Date: Tue, 05 Feb 2008 13:49

2 lines
1227 bytes

Tried without success to differentiate 1/x from first principles using delta 
x, can anyone help?

Re: differentiation from first principles

#100

Author: Virgil
Date: Tue, 05 Feb 2008 18:20

12 lines
1660 bytes

In article <6QZpj.1343$Jh5.286@newsfe4-win.ntli.net>,
 "sean�doyle" <sean.doyle4@virgin.net> wrote:

> 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

Re: differentiation from first principles

#101

Author: Ken Pledger
Date: Wed, 06 Feb 2008 23:47

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In article <Virgil-20F147.11202605022008@comcast.dca.giganews.com>,
 Virgil <Virgil@com.com> wrote:

> .... 
> [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.

Re: differentiation from first principles

#102

Author: Virgil
Date: Thu, 07 Feb 2008 01:16

18 lines
1819 bytes

In article <ken.pledger-5DBAAC.12471707022008@bats.mcs.vuw.ac.nz>,
 Ken Pledger <ken.pledger@mcs.vuw.ac.nz> wrote:

> In article <Virgil-20F147.11202605022008@comcast.dca.giganews.com>,
>  Virgil <Virgil@com.com> wrote:
> 
> > .... 
> > [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.

Thanks!

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