y = ln( tan(x/2) )"= 1/( tan(x/2) ) * ( tan(x/2) )"= 1/( tan(x/2) ) * ( sec^2(x/2) ) * (x/2)"= 1/( tan(x/2) ) * ( sec^2(x/2) ) * (1/2)= 1/( 2tan(x/2)*sec^2(x/2) )

y=tanx

y"=sec²x

所以y""=2secx*(secx)"

=2secx*secxtanx

=2sec²xtanx

(tan²x)′=2tanx(tanx)′

=2tanx(sinx/cosx)′

=2tanx×(cosxcosx+sinxsinx)/cos²x

=2tanx/cos²x。