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Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75111] Re: differentiate a function of a function
• From: "kem" <kemelmi at gmail.com>
• Date: Mon, 16 Apr 2007 20:28:21 -0400 (EDT)
• References: <evvbpf$bc1$1@smc.vnet.net>

On Apr 16, 11:23 am, "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

Thanks a lot!

As a followup, if my function is   g[x_,y_]:=Cos[t[x,y]+a[x,y]]
Tan[b[x,y]]
and I take in the same way derivative   TrigExpand[D[g[x,y],x]]
I get complicated expression that starts with

-Cos[t[x,y]] Sin[a[x,y]] Tan[b[x,y]] Derivative[1,0][a][x,y]-
Cos[a[x,y]] Sin[t[x,y]] Tan[b[x,y]] Derivative[1,0][a][x,y]+...

lets say that i know that
k = Cos[t[x,y]] Tan[b[x,y]]

how can i use this to simplify my result by substituting 'k' inside
like instead of every Cos[t[x,y]] Tan[b[x,y]] i put k ?

Thanks
kem