Hi, can anyone help me on this problem?

Suppose that instead of the usual definition of the derivative Df(x) , we define a new kind of derivative, D*f(x), by the forumla

D*f(x) = lim h---> 0 {f^2 (x+h) - f^2 ( x)}/h where f^2 (x) = [f(x)]^2

A) Derive formulas for computing the derivative D* of a sum, difference, product, and quotient. (only one solution is needed, from that I think I can figure out the rest)

B) Express D*f(x) in terms of Df(x)

Thanks