I have some function that depends on the variable x and a set of parameters x_i = x_1, x_2, ... .

[tex]f_i(x) = g(x,x_i)[/tex]

and then

[tex]y = min_i(f_i(x))[/tex]

So I'm finding the minimum value of f over all the x_i for some particular x value. Now I want to take dy/dx.

Is there some definition of min that allows differentiation? Like maybe calling it the [tex]\frac{1}{\infty}[/tex] norm. Although I don't think that would help since I probably can't differentiate infinite exponents. I don't think d/dx can pass through the min because that would just give me the minimum derivative value corresponding to one of the x_i, but what I want is how the minimum over all i changes as x moves relative to the x_i.

Any help?