Re: Is it possible?
- To: mathgroup at smc.vnet.net
- Subject: [mg72965] Re: Is it possible?
- From: dh <dh at metrohm.ch>
- Date: Fri, 26 Jan 2007 07:46:43 -0500 (EST)
- References: <firstname.lastname@example.org>
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. Daniel Travelmate wrote: > Hi, > > I'd really appreciate your help... > > I'been asked to perform a kind of analysis I've never done before..and > I'm not even sure that it's possible. > > Suppose you have value function V=v[x(a,b,c,d),y(....),z(......)] > > The key-parameter is 'a' and it turns out that the first and second > (partial) derivatives of V with respect to 'a' are negative and positive > respectively. (V is continous) > > Now there's a problem: I've been asked to invert V(a) (keeping b,c and d > constant)and to study the derivatives of this inverse function with > respect to b, c and d. I'm not sure it's possible to do such a thing. > ANd even if it is possible, I do not know how to start. > > Could you be so kind to tell me: > 1) if it is actually possible to perform this study; > 2) if the answer is yes, could you suggest me a starting point or any > reference? > > Thank you in advance >