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MathGroup Archive 2007

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Re: Is it possible?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72988] Re: Is it possible?
  • From: Travelmate <travelmate at where.com>
  • Date: Sat, 27 Jan 2007 06:41:49 -0500 (EST)
  • References: <epa2ic$iqn$1@smc.vnet.net> <epcoku$8gr$1@smc.vnet.net>

dh ha scritto:
> Hi,
> First, note that it does not matter how v depends on a internally. You 
> have a scalar function of one argument: y=f[x]. All you are asking for 
> is the derivative of the inverse function of a given function . The key 
> word here is "inverse function". The derivative of the inverse function 
> is the inverse of the derivative. Consider dy=f'[x] dx and you want 
> dx/dy=(dy/dx)^-1= 1/f'[x], This looks simple but there is a catch. The 
> formula gives you dx/dy as a function of x. If this is fine your are 
> done. However if you need a function of y you will need the inverse 
> function to f. In general this is hard, but you may be lucky and have a 
> simple case, all depends on the actual function. For the general case, 
> you can search for the key word "lagrage inversion theorem".
> Further, obviously, inversion is impossible in a region where f' is zero 
> somewhere.

Hi,

Thank you very much for your answer. I'll check out that theorem. At the 
moment, I'm exploring the possibility to use the implicit function 
theorem. In fact, I'm not working on an explicit function: the only 
thing I know about V(.) is something about its partial derivatives on 
the points of the region I need to study.

Thank you again.


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