Let f(x) be a real-valued function that is continuous on the closed interval [a, b] and let x_0 be a point in the open interval (a, b). If f(x) is one to one on [a, b] and differentiable at x_0 with f'(x_0)!=0, then f^(-1)(y) is differentiable at y_0 = f(x_0) and has a derivative at y_0 that satisfies (f^(-1))'(y_0) = 1/(f'(x_0))

derivative | one-to-one function | closed interval | open interval | continuous function | inverse function

John Herschel