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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: [mg75075] Re: [mg75071] differentiate a function of a function
  • From: leigh pascoe <leigh at cephb.fr>
  • Date: Mon, 16 Apr 2007 20:09:56 -0400 (EDT)
  • References: <200704160813.EAA09826@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
>
>
>
>
>
>   
Hi,

Taking some arbitrary functions for a and t (since you didn't specify), 
you could try:

a[x_,y_]:=3 x^2+y;
t[x_,y_]:=Exp[x-y];
eq1=D[Tan[t[x,y]+a[x,y]],x]==8

which gives

\!\(\((\[ExponentialE]\^\(x - y\) +
          6\ x)\)\ Sec[\[ExponentialE]\^\(x - y\) + 3\ x\^2 + y]\^2 
\[Equal]
    8\)


Is that what you are looking for? You can get the same result with the 
intermediate step

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

Leigh



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