Question: The function f with the domain: x is greater than 1/2 is defined by f(x)=4x(2x-1)^7. Given that f(1)=4, find the value of d/dx{f^-1(x)} when x=4.

I would try and find the inverse function of f(x), but im not sure how exactly this is related to integration in my textbook chapter. Can anyone shed some light as to which direction i proceed in finding d/dx{f^-1(x)}? Unsure how to start this one. Thanks