Re: differentiate a function of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75093] Re: differentiate a function of a function*From*: Bill Rowe <readnewsciv at sbcglobal.net>*Date*: Mon, 16 Apr 2007 20:19:09 -0400 (EDT)

On 4/16/07 at 4:13 AM, kemelmi at gmail.com (kem) wrote: >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)] You need to use proper Mathematica syntax to define f, i.e., f[x, y] = Tan[t[x, y] + a[x, y]]; Note the use of square brackets. Also, I've used the Mathematica syntax closest to what you have written. It may not be what you want. Alternatives are: f = Tan[t[x, y] + a[x, y]]; or f[x_, y_] := Tan[t[x, y] + a[x, y]]; This last is usually what you want when you define functions >2) take D[f,x] , such that also t(x,y) and a(x,y) will be also >differentiated Again, with the proper definition of f, Mathematica has no problem doing what you want. =46or example, In[4]:= f = Tan[t[x, y] + a[x, y]]; In[5]:= D[f, x] Out[5]= Sec[a[x, y] + t[x, y]]^2*(Derivative[1, 0][a][x, y] + Derivative[1, 0][t][x, y]) >3) be able to substitute these into some equation like: f_x f_xy = 8 The code posted above isn't an equation in Mathematica and it isn't obvious to me what you are trying to do here -- To reply via email subtract one hundred and four