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Re: differentiate a function of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg75109] Re: [mg75071] differentiate a function of a function
• From: kem <kemelmi at gmail.com>
• Date: Mon, 16 Apr 2007 20:27:20 -0400 (EDT)

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


On 4/16/07, Bob Hanlon <hanlonr at cox.net> wrote:
>
> f[x_,y_]:=Tan[t[x,y]+a[x,y]];
>
> D[f[x,y],x]
>
> Sec[a[x, y] + t[x, y]]^2*
>   (Derivative[1, 0][a][x, y] +
>    Derivative[1, 0][t][x, y])
>
>
> Bob Hanlon
>
> ---- kem <kemelmi 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
> >
> >
>
>