Let g(x) be the inverse of the function f(x) and f'(x) Then g'(x) is :
1 + (g(x))3
1 + (f(x))3
Since g(x) is the inverse of f(x)
(gof)(x) = x
g(f(x)) = x
g'(f(x)) f'(x) = 1
Hence (C) is correct answer.
Study 40% syllabus and score up to 100% marks in JEE