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Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75103] Re: differentiate a function of a function
• From: kem <kemelmi at gmail.com>
• Date: Mon, 16 Apr 2007 20:24:16 -0400 (EDT)

Thanks everybody ! it was very helpful.

kem


On 4/16/07, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
>
> kem wrote:
> > Hi,
> >
> > I was wondering how do I define a function in mathematica to be able
> > to differentiate it etc, where some of the parameters of this function
> > should be also a function. For example I want to be able to do the
> > following operations:
> >
> > 1) to say that f is a function: f(x,y) = Tan[t(x,y)+a(x,y)]
> >
> > 2) take D[f,x] , such that also t(x,y) and a(x,y) will be also
> > differentiated
> >
> > 3) be able to substitute these into some equation like: f_x f_xy = 8
> >
> > Thanks a lot
> >
> > kem
>
> In[1]:=
> t[x_, y_] := x^2 + x*y
> f[x_, y_] := Tan[t[x, y] + a[x, y]]
> D[f[x, y], x]
>
> Out[3]=
> Sec[x^2 + x*y + a[x, y]]^2*(2*x + y + Derivative[1, 0][a][x, y])
>
> Do you mean something like the above expressions?
>
>