Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75093] Re: differentiate a function of a function
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Mon, 16 Apr 2007 20:19:09 -0400 (EDT)

```On 4/16/07 at 4:13 AM, kemelmi at gmail.com (kem) wrote:

>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)]

You need to use proper Mathematica syntax to define f, i.e.,

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

Note the use of square brackets. Also, I've used the Mathematica
syntax closest to what you have written. It may not be what you
want. Alternatives are:

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

or

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

This last is usually what you want when you define functions

>2) take D[f,x] , such that also t(x,y) and a(x,y) will be also
>differentiated

Again, with the proper definition of f, Mathematica has no
problem doing what you want.

=46or example,

In[4]:=
f = Tan[t[x, y] + a[x, y]];

In[5]:=
D[f, x]

Out[5]=
Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] +
Derivative[1, 0][t][x, y])

>3) be able to substitute these into some equation like: f_x f_xy = 8

The code posted above isn't an equation in Mathematica and it
isn't obvious to me what you are trying to do here
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