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