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Re: differentiate a function of a function


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



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