Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75101] Re: differentiate a function of a function*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Mon, 16 Apr 2007 20:23:14 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <evvbpf$bc1$1@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 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?