Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75086] Re: [mg75071] differentiate a function of a function*From*: bsyehuda at gmail.com*Date*: Mon, 16 Apr 2007 20:15:34 -0400 (EDT)

f[x_,y_]:=Tan[t[x,y]+a[x,y]] D[f[x,y],x]//InputForm and this returns Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] + Derivative[1, 0][t][x, y]) so as you see the chain rule is used implicitly, as expected yehuda On 4/16/07, 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 > > >