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Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75086] Re: [mg75071] differentiate a function of a function
• From: bsyehuda at gmail.com
• Date: Mon, 16 Apr 2007 20:15:34 -0400 (EDT)

f[x_,y_]:=Tan[t[x,y]+a[x,y]]
D[f[x,y],x]//InputForm
and this returns
Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] +
  Derivative[1, 0][t][x, y])
so as you see the chain rule is used implicitly, as expected
yehuda


On 4/16/07, kem <kemelmi at gmail.com> 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
>
>
>