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MathGroup Archive 2007

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Re: differentiate a function of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75085] Re: [mg75071] differentiate a function of a function
  • From: anguzman at ing.uchile.cl
  • Date: Mon, 16 Apr 2007 20:15:03 -0400 (EDT)
  • References: <200704160813.EAA09826@smc.vnet.net>

Hello:

Well, if you define

f[x_, y_] = Tan[t[x, y] + a[x, y]];

then..
In[34]:=
D[f[t, u], t]

Out[34]=
Sec[a[t, u] + t[t, u]]^2*(Derivative[1, 0][a][t, u] +
    Derivative[1, 0][t][t, u])

In[52]:=
D[f[t, u], t, u]

Out[52]=
2*Sec[a[t, u] + t[t, u]]^2*Tan[a[t, u] + t[t, u]]*
    (Derivative[0, 1][a][t, u] + Derivative[0, 1][t][t,
      u])*(Derivative[1, 0][a][t, u] +
     Derivative[1, 0][t][t, u]) +
   Sec[a[t, u] + t[t, u]]^2*(Derivative[1, 1][a][t, u] +
     Derivative[1, 1][t][t, u])

you can put these expressions in Solve or Reduce in order to get 
information about solutions..
The diferentiation is performed using the chain rule. You can also check the
"Dt" function in Mathematica.

Atte. Andres Guzman





kem <kemelmi at gmail.com> ha escrito:

> 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
>
>
>



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