Derivative of inverse of a function

i think drawing the graph is the easiest solution
DON'T DRAW IT COMPLETELY
sketch a rough one by putting certain values of x
and an accurate one about x=∩

note that f(pi/2) = pi

thus f^-1(pi) = pi/2

thus we only have to find f'(pi/2) = 3

But aditya, the answer given is 1/3.
And aditya how did you get f'(pi/2) as 3?

f'(x) = 6(2x-pi)² + 2 + sinx

f'(pi/2) = 0 +2 +1 = 3

Hey Aditya am so sorry in the question actually we need to find derivative of f^-1(x) at x=pi.
So we need |d(f^-1(x))/dx| at x = pi.

f^-1(f(x)) = x

diff. w.r.t x ,

(f^-1(f(x))) ' * f'(x)= 1

here f(x) = pi
thus x=pi/2

thus (f^-1(pi)) ' = 1/f'(pi/2) = 1/3