let f(x)=(2x-pi)^3 + 2x - cosx

then vlue of d\dx(f^-1(x)) at x=pi is?

Dear student,

d/dx ( 1/f(x) = -f¹(x)/f(x)²

f¹(x) = 6*(2x-pi)^2 + 2 +sinx

f¹(pi) = 6pi²+2

f(pi) = pi^3 + 2pi + 1

d/dx ( 1/f(x) = -f¹(x)/f(x)² at x= pi => -(6pi²+2)/( pi^3 + 2pi + 1)^2

i hope this explains

but here...f^-1 means inverse function of f.........then what would be the answer?