Sage uses symbolic ring fot this. I guess you should just look how the
following is implemented and copy that disign:
sage: var('x')
x
sage: f=sin(x^2)
sage: f(x=2)
sin(4)
sage: f
sin(x^2)
sage: f.derivative()(x=2)
4*cos(4)
sage: f.derivative(7)
-128*x^7*cos(x^2) - 1344*x^5*sin(x^2) + 3360*x^3*cos(x^2) +
1680*x*sin(x^2)
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