If f(x) = the third root of (x-8), find the derivative of its inverse.
The derivative of its inverse = 1/f'(f^-1(x)) or 1 over its derivative at its inverse.
The Attempt at a Solution
I followed both the formula to verify my solution and also did some manual work in lieu of the formula. Basically, if g is the inverse of f, then f(g(x)) = x, and so the derivative of both sides is f'(g(x)g'(x) = 1, and since g'(x) is the derivative of the inverse of x, g'(x) = 1/f'(g(x)) and I get 3x^2. I have no idea if that's correct however. Note that g(x) = f^-1'(x); I'm typing g(x) since the latter notation gets messy really quickly when you don't bother to use LATEX. :p.