Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75080] Re: differentiate a function of a function*From*: "Norbert Marxer" <marxer at mec.li>*Date*: Mon, 16 Apr 2007 20:12:30 -0400 (EDT)*References*: <evvbpf$bc1$1@smc.vnet.net>

On 16 Apr., 10:23, "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 Hello If you evaluate the following: f[x_, y_] = Tan[a[x, y] + t[x, y]] D[f[x, y], x] D[f[x, y], x] + D[f[x, y], x, y] == 8 you will get: Out[1]= Tan[a[x, y] + t[x, y]] Out[2]= Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] + Derivative[1, 0][t][x, y]) Out[3]= Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] + Derivative[1, 0][t][x, y]) + 2*Sec[a[x, y] + t[x, y]]^2*Tan[a[x, y] + t[x, y]]* (Derivative[0, 1][a][x, y] + Derivative[0, 1][t][ x, y])*(Derivative[1, 0][a][x, y] + Derivative[1, 0][t][x, y]) + Sec[a[x, y] + t[x, y]]^2* (Derivative[1, 1][a][x, y] + Derivative[1, 1][t][ x, y]) == 8 If you run the select the above cells (in Mathematica) and convert them to TraditionalForm (e.g. click Ctrl+Shift+T or menu command Cell / ConvertTo / TraditionalForm) then you will get a nice display of the derivatives. Best Regards Norbert Marxer