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Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75101] Re: differentiate a function of a function
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 16 Apr 2007 20:23:14 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <evvbpf$bc1$1@smc.vnet.net>

kem 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

In[1]:=
t[x_, y_] := x^2 + x*y
f[x_, y_] := Tan[t[x, y] + a[x, y]]
D[f[x, y], x]

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

Do you mean something like the above expressions?