If g is the inverse of a function f and f'(x) = 1/(1+x⁵), then g'(x) is equal to

By the property of inverse we know that, f(g(x))=x where g(x) is the inverse of f(x). Now differentiating both the sides with respect to x, we get f'(g(x))g'(x)=1
g'(x)/(1+g(x)⁵)=1
g'(x)=1+g(x)⁵.