Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75075] Re: [mg75071] differentiate a function of a function*From*: leigh pascoe <leigh at cephb.fr>*Date*: Mon, 16 Apr 2007 20:09:56 -0400 (EDT)*References*: <200704160813.EAA09826@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 > > > > > > Hi, Taking some arbitrary functions for a and t (since you didn't specify), you could try: a[x_,y_]:=3 x^2+y; t[x_,y_]:=Exp[x-y]; eq1=D[Tan[t[x,y]+a[x,y]],x]==8 which gives \!\(\((\[ExponentialE]\^\(x - y\) + 6\ x)\)\ Sec[\[ExponentialE]\^\(x - y\) + 3\ x\^2 + y]\^2 \[Equal] 8\) Is that what you are looking for? You can get the same result with the intermediate step f[x_,y_]:=Tan[t[x,y]+a[x,y]]; D[f[x,y],x]==8 Leigh

**References**:**differentiate a function of a function***From:*"kem" <kemelmi@gmail.com>