Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75103] Re: differentiate a function of a function*From*: kem <kemelmi at gmail.com>*Date*: Mon, 16 Apr 2007 20:24:16 -0400 (EDT)

Thanks everybody ! it was very helpful. kem On 4/16/07, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote: > > 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? > >