I am working with interpolation function with some non-numerical arguments. A simplified version of the function I am working with is:

FUNC = Interpolation[{{0, a}, {1, b}, {2, c}}]

I would like to compute the derivative of FUNC with respect to a, b and c (for a general function value)

Potential solution: obtain the piecewise function that Interpolation generates. Problem: I do not know how to extract this piecewise function from FUNC.