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differentiate a function of a function


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

3) be able to substitute these into some equation like: f_x f_xy = 8

Thanks a lot


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