Finding the derivative of an inverse function. Let $f(x) = (-x^2)/(x^2+1)$. If g(x) is the inverse function of f(x) and f(1)=-1/2, what us g'(-1/2)?
Can someone explain how to do the above problem as I am not even sure where to start. Would I have to find the inverse of f(x) first or...

you have $$f(x) = -1 + \frac1{x^2 + 1}, \quad f(1) = -\frac 12, \quad f'(1) = -\frac14  $$  so the inverse function $g$ has $$g(-1/2) = 1, \quad g'(-1/2) = \frac1{f'(1)} = -4. $$
