Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: differentiate a function of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75080] Re: differentiate a function of a function
  • From: "Norbert Marxer" <marxer at mec.li>
  • Date: Mon, 16 Apr 2007 20:12:30 -0400 (EDT)
  • References: <evvbpf$bc1$1@smc.vnet.net>

On 16 Apr., 10:23, "kem" <keme... 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

Hello

If you evaluate the following:

f[x_, y_] = Tan[a[x, y] + t[x, y]]
D[f[x, y], x]
D[f[x, y], x] + D[f[x, y], x, y] == 8

you will get:

Out[1]=
Tan[a[x, y] + t[x, y]]

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

Out[3]=
Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] +
     Derivative[1, 0][t][x, y]) +
   2*Sec[a[x, y] + t[x, y]]^2*Tan[a[x, y] + t[x, y]]*
    (Derivative[0, 1][a][x, y] + Derivative[0, 1][t][
      x, y])*(Derivative[1, 0][a][x, y] +
     Derivative[1, 0][t][x, y]) +
   Sec[a[x, y] + t[x, y]]^2*
    (Derivative[1, 1][a][x, y] + Derivative[1, 1][t][
      x, y]) == 8

If you run the select the above cells (in Mathematica) and convert
them to TraditionalForm (e.g. click Ctrl+Shift+T or menu command
Cell / ConvertTo / TraditionalForm) then you will get a nice display
of the derivatives.

Best Regards
Norbert Marxer



  • Prev by Date: Re: differentiate a function of a function
  • Next by Date: Re: differentiate a function of a function
  • Previous by thread: Re: differentiate a function of a function
  • Next by thread: Re: differentiate a function of a function