Question is

" Use our knowledge that(f1)(x)=f(f1(x))1 to prove that dxd(tan1(x))=1+x21

Show all of the steps

I need to prove why the (tan^-1(x)) becomes 1/1+x² and I tried to prove it but I'm not sure if it's correct or not. Please tell me the step of making the prove. Please refer to the attached file

Q: use our knowledge that ( f ) ( x ) = FilFix) ) to prove that Show all of the steps Do (Tan' ( x ) ) = TAX 2 If f is the inverse of of then, Ja (f ( x 1 ) = _! f' ( f ( x ) ) # If Tan is the inverse of Tan then dx ( Tan (2) ) = 7+ x2 ( prove ) fox ) = Tan( x ) inverse of Tan (x ) * Tan ( x ) is g (x ) x ( Tan (9 ) = Sect Tan ( x ) ( Tah ) = Sec (x ) (9 ( x ) ) sect is gtx ) Tancy = 0 2 Tang = X () Hypo OPPE Adj plug in it to Ex ( Tan (x) ) dx ( Tantx ) ) = 1 1+ x 2