Mark M. answered 02/28/22
Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
By inspection, f(0) = 2. So (0,2) is on the graph of f and (2,0) is on the graph of f-1
f'(x) = 9x2 + 6cosx - 2sinx
f'(0) = 6 = slope of tangent line to the graph of f at the point (0,2)
So, [f-1(2)]' = 1 / f'(0) = 1/6 = slope of tangent line to the graph of f-1 at the point (2,0)