Re: is there any way to differentiate some functions including sigma^2 with respect to sigma^2 not sigma ?
- To: mathgroup at smc.vnet.net
- Subject: [mg38236] Re: is there any way to differentiate some functions including sigma^2 with respect to sigma^2 not sigma ?
- From: Tom Burton <tburton at brahea.com>
- Date: Tue, 10 Dec 2002 04:09:26 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello, On 12/4/02 12:22 AM, in article aske0m$kie$1 at smc.vnet.net, "Kimberly Damon yamin" <dykim92 at yahoo.com> wrote: > I tried to do but I can't. mathematica says sigma^2 is not a valid > variable." > is there any way to do that ? I can do that if I replace sigma^2 with > some variable and then differentiate it with respect to the some > variable not having power term. You can do this with the change rule. If the following example, f is a function of s, and g[s s] === f[x]. f[s_] = (Sin[t]*Cos[2*t])/s + 3*t^3 /. t -> s*s g[t_] = (Sin[t]*Cos[2*t])/Sqrt[t] + 3*t^3 Although we cannot find the derivative of f wrt s^2 directly, we can use the chain rule: d1 = f'[s]/D[s*s, s] To check the answer, for the equivalent derivative on g: d2 = g'[t] /. t -> s*s Simplify[PowerExpand[d1 - d2]] Hope this helps, Tom Burton